Hand initialization for machine learning based gesture recognition

ABSTRACT

The technology disclosed also initializes a new hand that enters the field of view of a gesture recognition system using a parallax detection module. The parallax detection module determines candidate regions of interest (ROI) for a given input hand image and computes depth, rotation and position information for the candidate ROI. Then, for each of the candidate ROI, an ImagePatch, which includes the hand, is extracted from the original input hand image to minimize processing of low-information pixels. Further, a hand classifier neural network is used to determine which ImagePatch most resembles a hand. For the qualified, most-hand like ImagePatch, a 3D virtual hand is initialized with depth, rotation and position matching that of the qualified ImagePatch.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNos. 62/335,542, entitled, “HAND INITIALIZATION FOR MACHINE LEARNINGBASED GESTURE RECOGNITION”, filed May 12, 2016 and 62/296,561, entitled,“IMAGE BASED TRACKING”, filed Feb. 17, 2016, both of which are herebyincorporated by reference for all purposes.

This application is related to U.S. patent application Ser. No.15/432,869, filed on Feb. 14, 2017 entitled, “MACHINE LEARNING BASEDGESTURE RECOGNITION,”. The related application is hereby incorporated byreference for all purposes.

This application is related to U.S. patent application Ser. No.15/432,872, filed on Feb. 14, 2017, entitled, “HAND POSE ESTIMATION FORMACHINE LEARNING BASED GESTURE RECOGNITION,”. The related application ishereby incorporated by reference for all purposes.

FIELD OF THE TECHNOLOGY DISCLOSED

The technology disclosed generally relates to using machine learning forestimating hand poses from raw hand images, and in particular relates tousing convolutional neural networks for regressing hand pose estimatesfrom input hand images.

BACKGROUND

The subject matter discussed in this section should not be assumed to beprior art merely as a result of its mention in this section. Similarly,a problem mentioned in this section or associated with the subjectmatter provided as background should not be assumed to have beenpreviously recognized in the prior art. The subject matter in thissection merely represents different approaches, which in and ofthemselves can also correspond to implementations of the claimedtechnology.

Conventional motion capture approaches rely on markers or sensors wornby the subject while executing activities and/or on the strategicplacement of numerous bulky and/or complex equipment in specialized andrigid environments to capture subject movements. Unfortunately, suchsystems tend to be expensive to construct. In addition, markers orsensors worn by the subject can be cumbersome and interfere with thesubject's natural movement. Further, systems involving large numbers ofcameras tend not to operate in real time, due to the volume of data thatneeds to be analyzed and correlated. Such considerations have limitedthe deployment and use of motion capture technology.

Consequently, there is a need for improved devices with greaterportability and techniques for capturing the motion of objects in realtime without fixed or difficult to configure sensors or markers.

Furthermore, the traditional paradigms of indirect interactions throughstandard input devices such as mouse, keyboard, or stylus have theirlimitations, including skewed fields of view and restrictively receptiveinterfaces. Particularly in the Augmented reality (AR) and virtualreality (VR) context, such traditional paradigms greatly diminish theuser experience. Accordingly, the technology disclosed allows users tointeract with the virtual interfaces generated in AR/VR environmentusing free-form in-air gestures. AR/VR technologies refers to the realtime registration of 2D or 3D computer generated imagery onto a liveview of a real world physical space or virtual space. A user is able toview and interact with the augmented and virtual imagery in such a wayas to manipulate the virtual objects in their view.

However, existing human-AR/VR systems interactions are very limited andunfeasible. Current AR/VR systems are complex as they force the user tointeract with AR/VR environment using a keyboard and mouse, or avocabulary of simply hand gestures. Further, despite strong academic andcommercial interest in AR/VR systems, AR/VR systems continue to becostly and requiring expensive equipment, and thus stand unsuitable forgeneral use by the average consumer.

An opportunity arises to provide an economical approach that providesadvantages of AR/VR for enhanced and sub-millimeter precisioninteraction with virtual objects without the draw backs of attaching ordeploying specialized hardware.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee. The color drawings also may be available in PAIRvia the Supplemental Content tab.

The included drawings are for illustrative purposes and serve only toprovide examples of possible structures and process operations for oneor more implementations of this disclosure. These drawings in no waylimit any changes in form and detail that may be made by one skilled inthe art without departing from the spirit and scope of this disclosure.A more complete understanding of the subject matter may be derived byreferring to the detailed description and claims when considered inconjunction with the following figures, wherein like reference numbersrefer to similar elements throughout the figures.

In the drawings, like reference characters generally refer to like partsthroughout the different views. Also, the drawings are not necessarilyto scale, with an emphasis instead generally being placed uponillustrating the principles of the technology disclosed. In thefollowing description, various implementations of the technologydisclosed are described with reference to the following drawings, inwhich:

FIG. 1 illustrates a training pipeline of one implementation of thetechnology disclosed.

FIG. 2 illustrates a testing pipeline of one implementation of thetechnology disclosed.

FIG. 3 shows one implementation of a fully connected neural network withmultiple layers.

FIG. 4 depicts a block diagram of training a convolutional neuralnetwork in accordance with one implementation of the technologydisclosed.

FIGS. 5A and 5B show one implementation of ground truth hand poseestimates with twenty-eight (28) joint locations of the hand inthree-dimensions (3D).

FIG. 6 is one implementation of sub-sampling layers in accordance withone implementation of the technology disclosed.

FIG. 7 shows one implementation of non-linear layers in accordance withone implementation of the technology disclosed.

FIG. 8 depicts one implementation of a two-layer convolution of theconvolution layers.

FIG. 9 illustrates real images of two sets of sixteen (16) 3×3convolution kernels learned and used for feature extraction fromstereoscopic images.

FIG. 10 illustrates a real image of the resulting feature map producedby the convolution kernels shown in FIG. 9 .

FIG. 11 illustrates how the learned convolution kernels applied locallyto an input image (on the left) produce a convolved image (on the right)that is robust to the background and the clutter.

FIG. 12 depicts one implementation of a principal component analysis(PCA) basis used for feature extraction in accordance with oneimplementation of the technology disclosed.

FIG. 13 illustrates one implementation of a fully connected masternetwork or a fully connected expert network.

FIG. 14 depicts one implementation of three (3) master networks that aretrained on different versions of training data created by the validationdata split.

FIG. 15 shows one implementation of partitioning training data on whichexpert networks are trained.

FIG. 16 illustrates one implementation of synergy between the masternetworks and expert networks during testing.

FIG. 17 illustrates one implementation of a pose space of training datain an eighty-four (d1-d84) dimensional coordinate system representingeighty-four (84) dimensional hand poses comprised of twenty-eight (28)3D (x₀, y₀, z₀) hand joints.

FIG. 18 illustrates one implementation of a clustered pose space.

FIG. 19 shows one implementation of synergy between master networks andexpert networks in pose space.

FIG. 20 shows a representative method of synergy between atemporalmaster networks and atemporal expert networks in accordance with oneimplementation of the technology disclosed.

FIG. 21 is one implementation of training temporal master networks andtemporal expert networks.

FIG. 22 is one implementation of using temporal master networks andtemporal expert networks during testing/tracking.

FIG. 23 illustrates one implementation of temporal master networks andtemporal expert networks serving as recurrent neural networks (RNNs)based on long short term memory (LSTM).

FIG. 24 shows a representative method of synergy between temporal masternetworks and temporal expert networks in accordance with oneimplementation of the technology disclosed.

FIG. 25 shows one implementation of a probability distribution function(sample covariance matrix) that illustrates outlier-robust covariancepropagation in accordance with one implementation of the technologydisclosed.

FIG. 26 illustrates the probabilities of the distances of 3D jointestimates (circles) in current frame from the probability distributionfunction (sample covariance matrix) calculated in FIG. 25 .

FIG. 27 shows one implementation of a sample covariance matrixpropagated from a prior frame to a current frame.

FIG. 28 shows one implementation of a plurality of 3D joint locationestimates produced by a plurality of expert networks for a single handjoint.

FIG. 29 illustrates one implementation of a covariance distribution andmean calculated for 3D joint location estimates.

FIG. 30 depicts one implementation of new 3D joint location estimatesproduced by a plurality of expert networks for the same hand jointsshown in FIGS. 28 and 29 .

FIG. 31 shows one implementation of determination of inlier and outlier3D joint location estimates.

FIGS. 32A, 32B, 32C and 32D show a temporal sequence of theoutlier-robust covariance propagations simultaneously and concurrentlycalculated for all twenty-eight (28) joints of the hand.

FIG. 33 shows a representative method of hand pose estimation usingoutlier-robust covariance propagation in accordance with oneimplementation of the technology disclosed.

FIG. 34 illustrates one implementation of a fitted hand based on the 3Djoint locations of the twenty-eight (28) hand joints.

FIG. 35A illustrates one implementation of spatial normalization.

FIG. 35B depicts one implementation of a rotated and extractedImagePatch.

FIG. 35C shows other examples of extracted ImagePatches.

FIG. 35D is one implementation of a 3D virtual hand initialized for anImagePatch shown in FIG. 35B.

FIG. 36 shows one implementation of ImageRects fitted on an ImagePatch.

FIG. 37 is one implementation of extrapolating a previous frame's fittedhand model into a current frame.

FIG. 38 shows a representative method of initialization of a hand inaccordance with one implementation of the technology disclosed.

FIGS. 39A, 39B, 39C, 39D, 39E, 39F, 39G, 39H, 39I, 39J, 39K, 39L, 39M,39N and 39O show multiple frames in a time continuous gesture sequenceof hand poses represented by skeleton hand models fitted to jointcovariances in for the gesture sequences.

FIGS. 40A, 40B and 40C show one implementation of skeleton hand modelsfitted to estimated joint covariances interacting with and manipulatingvirtual objects (e.g., depicted boxes) in an augmented reality(AR)/virtual reality (VR) environment.

FIG. 41 depicts one implementation of a computer graphic simulator thatprepares sample simulated hand positions of gesture sequences fortraining of neural networks.

FIG. 42 illustrates a graphical user interface (GUI) implementation of acomputer graphics simulator visually rendering gesture sequence objectsfor configuration and specification.

FIG. 43 illustrates a graphical user interface (GUI) implementation of acomputer graphics simulator visually rendering device, image, hand andscene attributes for configuration and specification.

FIG. 44 illustrates a graphical user interface (GUI) implementation of acomputer graphics simulator visually displaying rendering attributes forconfiguration and specification.

FIG. 45 illustrates a graphical user interface (GUI) implementation of acomputer graphics simulator visually rendering hand attributes forconfiguration and specification.

FIG. 46 shows one implementation of a start key frame of a simulatedgesture sequence generated by a computer graphic simulator.

FIG. 47 shows one implementation of an intermediate key frame of asimulated gesture sequence generated by a computer graphic simulator.

FIG. 48 shows one implementation of a terminal key frame of a simulatedgesture sequence generated by a computer graphic simulator.

FIG. 49 is one implementation of simulated hand images in the form ofgrayscale stereoscopic or binocular images based on a simulated 3D meshhand model.

FIG. 50 shows one implementation of generating simulated hand poses andgesture sequences as 3D capsule hand models using a computer graphicsimulator.

FIG. 51 illustrates one implementation of modification of a simulationparameter in a given key frame of simulated hand poses and gesturesequences generated as 3D capsule hand models.

FIG. 52 is one implementation of simulated hand images in the form ofgrayscale stereoscopic or binocular images based on a simulated 3Dcapsule hand model.

FIGS. 53A, 53B, 53C, 53D, 53E, 53F, 53G, 53H, 53I, 53J and 53K aredifferent examples of automated range-based simulations of differenthand poses generated by a computer graphics simulator.

FIG. 54 shows one implementation of simulated hand images (left andright, (l, r)) generated by a computer graphics simulator andcorresponding label assigned or mapped to the images in the form of theground truth 84 (28×3) dimensional pose vector of 3D joint locations oftwenty-eight (28) hand joints.

FIG. 55 shows a representative method of generating training data inaccordance with one implementation of the technology disclosed.

FIG. 56 illustrates an augmented reality (AR)/virtual reality (VR)environment with a gesture recognition system for capturing image dataaccording to one implementation of the technology disclosed.

FIG. 57 shows a simplified block diagram of a computer system forimplementing a gesture recognition system.

INTRODUCTION

A Human hand is a non-rigid articulated structure that changes in shapein various ways, making it an intricate and complex object. The humanhand is made up of 27 bones, numerous muscles, tendons and ligamentsthat provide it 30-50 degrees of freedom and varying constrains onmotion and flexibility. However, motion ability, visual attribute andstructure of a hand vary significantly between individuals. As well, thehand is also subject to complex occlusion, both caused by the handitself (self-occlusion), e.g. from crossing ones fingers or clinchingthe hand into a closed fist, and from other objects that the hand isinteracting with, e.g. grasping an object. In addition, the fingers areadjacent to other that leads to self-occlusions. Also, a hand has manyself-similar parts (e.g., fingers) and large variations in terms ofshape, size and skin tone. Further, because hand postures and gesturesare highly variable from one person to another, it is a challenge tocapture the invariant properties of the hands and use this informationto represent them. Moreover, the human hand is capable of an enormousrange of poses, which are also difficult to simulate or to account for.

While humans are able to naturally detect the presence and pose of handeven during complex gestures and strong occlusion, the task isrelatively difficult for machines and computer vision systems comparedto e.g. face detection and head pose estimation. This is because thecomplex and articulated structure of the hand makes the mapping fromhand appearance in an image to pose estimation highly non-linear. Thehigh level of non-linearity makes the task difficult for classic featurebased machine learning methods.

However, in recent years, machine learning methods capable of performingdeep learning have been used for hand detection and pose estimation.Supervised learning is based on the system trying to predict outcomesfor known examples and is a commonly used training method. It comparesits predictions to the target answer and “learns” from its mistakes. Thedata start as inputs to the input layer neurons. The neurons pass theinputs along to the next nodes. As inputs are passed along, theweighting, or connection, is applied and when the inputs reach the nextnode, the weightings are summed and either intensified or weakened. Thiscontinues until the data reaches the output layer where the modelpredicts an outcome. In a supervised learning system, the predictedoutput is compared to the actual output for that case. If the predictedoutput is equal to the actual output, no change is made to the weightsin the system. But, if the predicted output is higher or lower than theactual outcome in the data, the error is propagated back through thesystem and the weights are adjusted accordingly. This feeding errorsbackwards through the network is called “back propagation.” Both themulti-layer perceptron and the radial basis function are supervisedlearning techniques. The multi-layer perceptron uses theback-propagation while the radial basis function is a feed-forwardapproach which trains on a single pass of the data.

Deep learning refers to a subfield of machine learning that is based onlearning levels of representations, corresponding to a hierarchy offeatures, factors or concepts, where higher-lever concepts are definedfrom lower-lever ones, and the same lower-lever concepts define manyhigher-lever concepts. Deep learning is learning multiple levels ofrepresentation and abstraction of data such as images, audio and text.The concept of deep learning comes from the study of artificial neuralnetworks, and in particular from deep neural networks with multilayerperceptron that forms many hidden layers of a deep learning structure.

The technology disclosed provides a new architecture for human hand poseestimation using multi-layer convolutional neural networks and newlearning techniques that demonstrate improvement over the current, stateof the art gesture recognition architectures. In particular, thetechnology disclosed applies convolutional neural networks to thetechnical problem of hand detection and hand pose estimation. Theconvolutional neural networks are trained to perform regression oversimulated data generated from images in the order of 100,000 and abillion. The systems and methods to generate the simulated data are alsodisclosed. The disclosed convolutional neural networks are fullyconnected deep neural networks that perform end to end feature learningand are trained with the back propagation algorithm.

The technology disclosed introduces two types of neural networks:“master” or “generalists” networks and “expert” or “specialists”networks. Both, master networks and expert networks, are fully connectedneural networks that take a feature vector of an input hand image andproduce a prediction of the hand pose. Master networks and expertnetworks differ from each other based on the data on which they aretrained. In particular, master networks are trained on the entire dataset. In contrast, expert networks are trained only on a subset of theentire dataset. In regards to the hand poses, master networks aretrained on the input image data representing all available hand posescomprising the training data (including both real and simulated handimages). Expert networks are individually trained on specific classes ofhand poses such as open-hand poses, first poses, grab poses, V-shapedposes or pinch poses. This distinction allows the convolutional neuralnetworks to have “generalists” in the form of master networks that aretrained over the entire available training data, which nearly cover thespace of all possible poses and hence generalize better over unseen handposes, not present in the training data. Furthermore, within each of themaster networks and expert networks, there are two kinds of neuralnetworks: “temporal” networks and “atemporal” networks. The temporalnetworks also take into account prior pose information when predicting anew pose.

The technology disclosed performs hand pose estimation on a so-called“joint-by-joint” basis. So, when a plurality of estimates for the 28hand joints are received from a plurality of expert networks (and frommaster experts in some high-confidence scenarios), the estimates areanalyzed at a joint level and a final location for each joint iscalculated based on the plurality of estimates for a particular joint.This is a novel solution discovered by the technology disclosed becausenothing in the field of art determines hand pose estimates at suchgranularity and precision. Regarding granularity and precision, becausehand pose estimates are computed on a joint-by-joint basis, this allowsthe technology disclosed to detect in real time even the minutest andmost subtle hand movements, such a bend/yaw/tilt/roll of a segment of afinger or a tilt an occluded finger, as demonstrated supra in theExperimental Results section of this application.

Further, the outlier-robust covariance propagation prevents erroneous orless accurate estimates from influencing the final hand pose estimates.For instance, if out of thirty (30) expert networks 112, twenty-seven(27) give erroneous estimates that are detected as outliers, then thatwould not negatively influences the estimation of the final hand poseand the three (3) correct and accurate estimates, that were detected asinliers, would dominate the final hand pose estimation.

The technology disclosed also initializes a new hand that enters thefield of view of a gesture recognition system using a parallax detectionmodule. The parallax detection module determines candidate regions ofinterest (ROI) for a given input hand image and computes depth, rotationand position information for the candidate ROI. Then, for each of thecandidate ROI, an ImagePatch, which includes the hand, is extracted fromthe original input hand image to minimize processing of low-informationpixels. Further, a hand classifier neural network is used to determinewhich ImagePatch most resembles a hand. For the qualified, most-handlike ImagePatch, a 3D virtual hand is initialized with depth, rotationand position matching that of the qualified ImagePatch.

The technology disclosed also discloses a computer graphics simulatorthat automatically generates simulated hand poses and gesture sequencesin the order of 100,000 and a billion. The hand poses and gesturesequences are generated across a variety of simulation parameters thatrepresent various anatomical features and motions of a real hand. Also,a range-based automation is employed that includes instantiating aplurality of simulation parameters between a range of anatomicallycorrect hand poses and gesture sequences to automatically generatenumerous hand poses and gesture sequences between the ranges. Inaddition, various backgrounds, rendering models and noises are appliedto the hand poses and gesture sequences to better represent the space ofall possible hand poses and gestures.

System and methods in accordance herewith generally utilize informationabout the motion of a control object, such as a user's hand, finger or astylus, in three-dimensional (3D) space to operate a physical or virtualuser interface and/or components thereof based on the motioninformation. Various implementations take advantage of motion-capturetechnology to track the motions of the control object in real time (ornear real time, i.e., sufficiently fast that any residual lag betweenthe control object and the system's response is unnoticeable orpractically insignificant). Other implementations can use syntheticmotion data (e.g., generated by a computer game) or stored motion data(e.g., previously captured or generated). References to motions in“free-form in-air”, “free-space”, “in-air”, or “touchless” motions orgestures are used herein with reference to an implementation todistinguish motions tied to and/or requiring physical contact of themoving object with a physical surface to effect input; however, in someapplications, the control object can contact a physical surfaceancillary to providing input, in such case the motion is stillconsidered a “free-form in-air” motion.

Further, in some implementations, a virtual environment can be definedto co-reside at or near a physical environment. For example, a virtualtouch screen can be created by defining a (substantially planar) virtualsurface at or near the screen of a display, such as an HMD, television,monitor, or the like. A virtual active table top can be created bydefining a (substantially planar) virtual surface at or near a table topconvenient to the machine receiving the input.

Among other aspects, implementations can enable quicker, crisper gesturebased or “free-form in-air” (i.e., not requiring physical contact)interfacing with a variety of machines (e.g., a computing systems,including HMDs, smart phones, desktop, laptop, tablet computing devices,special purpose computing machinery, including graphics processors,embedded microcontrollers, gaming consoles, audio mixers, or the like;wired or wirelessly coupled networks of one or more of the foregoing,and/or combinations thereof), obviating or reducing the need forcontact-based input devices such as a mouse, joystick, touch pad, ortouch screen.

Implementations of the technology disclosed also relate to methods andsystems that facilitate free-form in-air gestural interactions in avirtual reality (VR) and augmented reality (AR) environment. Thetechnology disclosed can be applied to solve the technical problem ofhow the user interacts with the virtual screens, elements, or controlsdisplayed in the AR/VR environment. Existing AR/VR systems restrict theuser experience and prevent complete immersion into the real world bylimiting the degrees of freedom to control virtual objects. Whereinteraction is enabled, it is coarse, imprecise, and cumbersome andinterferes with the user's natural movement. Such considerations ofcost, complexity and convenience have limited the deployment and use ofAR technology.

The systems and methods described herein can find application in avariety of computer-user-interface contexts, and can replace mouseoperation or other traditional means of user input as well as providenew user-input modalities. Free-form in-air control object motions andvirtual-touch recognition can be used, for example, to provide input tocommercial and industrial legacy applications (such as, e.g., businessapplications, including Microsoft Outlook™; office software, includingMicrosoft Office™, Windows™, Excel, etc.; graphic design programs;including Microsoft Visio™ etc.), operating systems such as MicrosoftWindows™; web applications (e.g., browsers, such as Internet Explorer™);other applications (such as e.g., audio, video, graphics programs,etc.), to navigate virtual worlds (e.g., in video games) or computerrepresentations of the real world (e.g., Google Street View™), or tointeract with three-dimensional virtual objects (e.g., Google Earth™).In some implementations, such applications can be run on HMDs or otherportable computer devices and thus can be similarly interacted withusing the free-form in-air gestures.

A “control object” or “object” as used herein with reference to animplementation is generally any three-dimensionally movable object orappendage with an associated position and/or orientation (e.g., theorientation of its longest axis) suitable for pointing at a certainlocation and/or in a certain direction. Control objects include, e.g.,hands, fingers, feet, or other anatomical parts, as well as inanimateobjects such as pens, styluses, handheld controls, portions thereof,and/or combinations thereof. Where a specific type of control object,such as the user's finger, is used hereinafter for ease of illustration,it is to be understood that, unless otherwise indicated or clear fromcontext, any other type of control object can be used as well.

A “virtual environment,” may also referred to as a “virtual construct,”“virtual touch plane,” or “virtual plane,” as used herein with referenceto an implementation denotes a geometric locus defined (e.g.,programmatically) in space and useful in conjunction with a controlobject, but not corresponding to a physical object; its purpose is todiscriminate between different operational modes of the control object(and/or a user-interface element controlled therewith, such as a cursor)based on whether the control object interacts the virtual environment.The virtual environment, in turn, can be, e.g., a virtual environment (aplane oriented relative to a tracked orientation of the control objector an orientation of a screen displaying the user interface) or a pointalong a line or line segment extending from the tip of the controlobject.

Using the output of a suitable motion-capture system or motioninformation received from another source, various implementationsfacilitate user input via gestures and motions performed by the user'shand or a (typically handheld) pointing device. For example, in someimplementations, the user can control the position of a cursor and/orother object on the interface of an HMD by with his index finger in thephysical environment outside the HMD's virtual environment, without theneed to touch the screen. The position and orientation of the fingerrelative to the HMD's interface, as determined by the motion-capturesystem, can be used to manipulate a cursor symbol. As will be readilyapparent to one of skill in the art, many other ways of mapping thecontrol object position and/or orientation onto a screen location can,in principle, be used; a particular mapping can be selected based onconsiderations such as, without limitation, the requisite amount ofinformation about the control object, the intuitiveness of the mappingto the user, and the complexity of the computation. For example, in someimplementations, the mapping is based on intersections with orprojections onto a (virtual) plane defined relative to the camera, underthe assumption that the HMD interface is located within that plane(which is correct, at least approximately, if the camera is correctlyaligned relative to the screen), whereas, in other implementations, thescreen location relative to the camera is established via explicitcalibration (e.g., based on camera images including the screen).

Aspects of the system and methods, described herein provide for improvedmachine interface and/or control by interpreting the motions (and/orposition, configuration) of one or more control objects or portionsthereof relative to one or more virtual environments disposed (e.g.,programmatically) at least partially within a field of view of animage-capture device. In implementations, the position, orientation,and/or motion of control object(s) (e.g., a user's finger(s), thumb,etc.; a suitable hand-held pointing device such as a stylus, wand, orsome other control object; portions and/or combinations thereof) aretracked relative to the virtual environment to facilitate determiningwhether an intended free-form in-air gesture has occurred. Free-formin-air gestures can include engaging with a virtual control (e.g.,selecting a button or switch), disengaging with a virtual control (e.g.,releasing a button or switch), motions that do not involve engagementwith any virtual control (e.g., motion that is tracked by the system,possibly followed by a cursor, and/or a single object in an applicationor the like), environmental interactions (i.e., gestures to direct anenvironment rather than a specific control, such as scroll up/down),special-purpose gestures (e.g., brighten/darken screen, volume control,etc.), as well as others or combinations thereof.

Free-form in-air gestures can be mapped to one or more virtual controls,or a control-less screen location, of a display device associated withthe machine under control, such as an HMD. Implementations provide formapping of movements in three-dimensional (3D) space conveying controland/or other information to zero, one, or more controls. Virtualcontrols can include imbedded controls (e.g., sliders, buttons, andother control objects in an application), or environmental-levelcontrols (e.g., windowing controls, scrolls within a window, and othercontrols affecting the control environment). In implementations, virtualcontrols can be displayable using two-dimensional (2D) presentations(e.g., a traditional cursor symbol, cross-hairs, icon, graphicalrepresentation of the control object, or other displayable object) on,e.g., one or more display screens, and/or 3D presentations usingholography, projectors, or other mechanisms for creating 3Dpresentations. Presentations can also be audible (e.g., mapped tosounds, or other mechanisms for conveying audible information) and/orhaptic.

As used herein, a given signal, event or value is “responsive to” apredecessor signal, event or value of the predecessor signal, event orvalue influenced by the given signal, event or value. If there is anintervening processing element, step or time period, the given signal,event or value can still be “responsive to” the predecessor signal,event or value. If the intervening processing element or step combinesmore than one signal, event or value, the signal output of theprocessing element or step is considered “responsive to” each of thesignal, event or value inputs. If the given signal, event or value isthe same as the predecessor signal, event or value, this is merely adegenerate case in which the given signal, event or value is stillconsidered to be “responsive to” the predecessor signal, event or value.“Responsiveness” or “dependency” or “basis” of a given signal, event orvalue upon another signal, event or value is defined similarly.

As used herein, the “identification” of an item of information does notnecessarily require the direct specification of that item ofinformation. Information can be “identified” in a field by simplyreferring to the actual information through one or more layers ofindirection, or by identifying one or more items of differentinformation which are together sufficient to determine the actual itemof information. In addition, the term “specify” is used herein to meanthe same as “identify.”

Among other aspects, the technology described herein with reference toexample implementations can provide for automatically (e.g.,programmatically) cancelling out motions of a movable sensor configuredto capture motion and/or determining the path of an object based onimaging, acoustic or vibrational waves. Implementations can enablegesture detection, virtual reality and augmented reality, and othermachine control and/or machine communications applications usingportable devices, e.g., head mounted displays (HMDs), wearable goggles,watch computers, smartphones, and so forth, or mobile devices, e.g.,autonomous and semi-autonomous robots, factory floor material handlingsystems, autonomous mass-transit vehicles, automobiles (human or machinedriven), and so forth, equipped with suitable sensors and processorsemploying optical, audio or vibrational detection. In someimplementations, projection techniques can supplement the sensory basedtracking with presentation of virtual (or virtualized real) objects(visual, audio, haptic, and so forth) created by applications loadableto, or in cooperative implementation with, the HMD or other device toprovide a user of the device with a personal virtual experience (e.g., afunctional equivalent to a real experience).

Some implementations include optical image sensing. For example, asequence of images can be correlated to construct a 3-D model of theobject, including its position and shape. A succession of images can beanalyzed using the same technique to model motion of the object such asfree-form gestures. In low-light or other situations not conducive tooptical imaging, where free-form gestures cannot be recognized opticallywith a sufficient degree of reliability, audio signals or vibrationalwaves can be detected and used to supply the direction and location ofthe object as further described herein.

DETAILED DESCRIPTION

FIG. 1 illustrates a training pipeline 100 of one implementation of thetechnology disclosed. Training pipeline 100 includes training data 102,pre-processing 103, convolution layers 104, sub-sampling layers 106,non-linear layers 108, master networks 110, expert networks 112, poseestimation 114 and hand model fitting 116. Pipeline 100 can beimplemented at least partially with a computer or other data processingsystem, e.g., by one or more processors configured to receive orretrieve information, process the information, store results, andtransmit the results. Other implementations may perform the actions indifferent orders and/or with different, fewer or additional actions thanthose illustrated in FIG. 1 . Multiple actions can be combined in someimplementations. For convenience, this pipeline is described withreference to the system that carries out a method. The system is notnecessarily part of the method.

FIG. 2 illustrates a testing pipeline 200 of one implementation of thetechnology disclosed. Testing pipeline 200 includes testing data 202,initialization 206, pre-processing 103, convolution layers 104,sub-sampling layers 106, non-linear layers 108, master networks 110,expert networks 112, pose estimation 114, hand model fitting 116 andaugmented reality (AR) and/or virtual reality (VR) interaction 208. Inthis application, “testing” or “testing pipeline 200” refers to realtime tracking of a hand, i.e., “tracking,” which is done by feeding theconvolutional neural network 101 real world hand images captured by agesture recognition system at run time. Pipeline 200 can be implementedat least partially with a computer or other data processing system,e.g., by one or more processors configured to receive or retrieveinformation, process the information, store results, and transmit theresults. Other implementations may perform the actions in differentorders and/or with different, fewer or additional actions than thoseillustrated in FIG. 2 . Multiple actions can be combined in someimplementations. For convenience, this pipeline is described withreference to the system that carries out a method. The system is notnecessarily part of the method.

Convolutional Neural Network

FIG. 3 shows one implementation of a fully connected neural network 300with multiple layers. Neural network 300 is a system of interconnectedartificial neurons (e.g., a₁, a₂, a₃) that exchange messages betweeneach other. Specifically, neural network 300 has three inputs, twoneurons in the hidden layer and two neurons in the output layer. Thehidden layer has an activation function ƒ(⋅) and the output layer has anactivation function g(⋅). The connections have numeric weights (e.g.,w₁₁, w₂₁, w₁₂, w₃₁, w₂₂, w₃₂, v₁₁, v₂₂) that are tuned during thetraining process, so that a properly trained network responds correctlywhen fed an image to recognize. The input layer processes the raw inputfed to the convolutional neural network 101, the hidden layer processesthe output from the input layer based on the weights of the connectionsbetween the input layer and the hidden layer. The output layer takes theoutput from the hidden layer and processes it based on the weights ofthe connections between the hidden layer and the output layer. Thenetwork includes multiple layers of feature-detecting neurons. Eachlayer has many neurons that respond to different combinations of inputsfrom the previous layers. These layers are constructed so that the firstlayer detects a set of primitive patterns in the input image data, thesecond layer detects patterns of patterns and the third layer detectspatterns of those patterns.

Convolutional neural network 101 is a special type of neural network.Convolutional neural network 101 learns highly non-linear mappings byinterconnecting layers of artificial neurons arranged in many differentlayers with activation functions that make the layers dependent. Itincludes one or more convolutional layers 104, with one or moresub-sampling layers 106 and non-linear layers 108, which are followed byone or more fully connected layers 118 as in a neural network. Eachelement of convolutional neural network 101 receives inputs from a setof features in the previous layer. Specifically, convolutional neuralnetwork 101 learns concurrently because the neurons in the same featuremap have identical weights. These local shared weights reduce thecomplexity of the network such that when multi-dimensional input imagedata enters the network, convolutional neural network 101 avoids thecomplexity of data reconstruction in feature extraction and regressionor classification process.

Training a Convolutional Neural Network

FIG. 4 depicts a block diagram of training 400 a convolutional neuralnetwork 101 in accordance with one implementation of the technologydisclosed. Convolutional neural network 101 is adjusted or trained sothat particular input image data 402 (e.g., binocular images) lead to aspecific target hand pose estimates 406. Convolutional neural network101 is adjusted 410 using back propagation 408 based on a comparison ofthe output 404 and the target 406 until the network output 404 matchesthe target 406. Convolutional neural network 101 is trained usinglabeled dataset 500A and 500B in a wide assortment of representativeinput image patterns that are mapped to their intended output 406 ofground truth hand pose estimates 500A. The target hand pose estimates500A are labeled with twenty-eight (28) joint locations of the hand inthree-dimensions (3D). One implementation of the ground truth hand pose500A with twenty-eight joint locations in 3D is graphically illustratedin FIGS. 5A and 5B. In some implementations, the points for the fingersand thumb are located at the endpoints of the bones, from the tip of thedistal bone down to where the metacarpals meet the wrist. As shown inFIG. 5B, the ground truth hand pose 500A is labeled with twenty-eight 3Djoint locations 500B. The twenty-eight joints include four joints forthe thumb, five joints for each of the index, middle, ring and pinkiefingers and four joints for the wrist or arm. In other implementations,the actual output and the ground truth desired output are not in jointspace but instead in angle space. In such an implementation, the targethand pose estimates are labeled with joint angles. In yet otherimplementations, the actual output and the ground truth desired outputare in the form of capsule hand models, skeleton hand models, volumetrichand models and/or mesh hand models, muscle hand models, each in 2Dand/or 3D space.

Learning 400 in convolutional neural network 101 is done by adjusting410 the weights by the difference between the desired target hand poseestimates 406 and the actual output hand pose estimates 410. This ismathematically described as:Δw _(i) =x _(i)δ

-   -   where δ=(desired output)−(actual output)

During learning 400, convolutional neural network 101 adjusts theweights to generate the desired output, or target hand pose estimates406, given some inputs like input image data 402 that generate thatspecific target. In one implementation, the learning rule is defined as:w _(nm) ←w _(nm)+α(t _(m)−φ_(m))a _(n)

In the equation above: the arrow indicates an update of the value; t_(m)is the target value of neuron m; φ_(m) is the computed current output ofneuron m; a_(n) is input n; and α is the learning rate.

The intermediary step in learning 400 includes generating a featurevector from input image data 402 using convolution layers 104. Thefeature vector is then fed to the fully connected layers 118, where theactivation of all the neurons in the fully connected layers is computedand stored to generate an output, i.e. prediction of twenty-eight (28)joint locations of a hand in 3D. This referred to as the forward pass,or going forward. Then, an error 412 between the output prediction 404and the desired target 406 is measured. Advancing further, the gradientwith respect to the weights in each layer, starting at the output, iscalculated. This is referred to as the backward pass, or goingbackwards. The weights in the network are updated using a combination ofthe negative gradient and previous weights.

In one implementation, convolutional neural network 101 uses analgorithm that performs backward propagation of errors by means ofgradient descent. One example of a sigmoid function based backpropagation algorithm is described below:

$\varphi = {{f(h)} = \frac{1}{1 + e^{- h}}}$

In the sigmoid function above, h is the weighted sum computed by aneuron. The sigmoid function has the following derivative:

$\frac{\partial\varphi}{\partial h} = {\varphi\left( {1 - \varphi} \right)}$

The algorithm includes computing the activation of all neurons in thenetwork, yielding an output for the forward pass. The activation ofneuron m in the hidden layers is described as:

$\varphi_{m} = \frac{1}{1 + e^{- {hm}}}$$h_{m} = {\sum\limits_{n = 1}^{N}{a_{n}w_{nm}}}$

This is done for all the hidden layers to get the activation describedas:

$\varphi_{k} = \frac{1}{1 + e^{hk}}$$h_{k} = {\sum\limits_{m = 1}^{M}{\varphi_{m}v_{mk}}}$

Then, the error and the correct weights are calculated per layer. Theerror at the output is computed as:δ_(ok)=(t _(k)−φ_(k))φ_(k)(1−φ_(k))

The error in the hidden layers is calculated as:

$\delta_{hm} = {{\varphi_{m}\left( {1 - \varphi_{m}} \right)}{\sum\limits_{k = 1}^{K}{v_{mk}\delta_{ok}}}}$

The weights of the output layer are updated as:v _(mk) ←v _(mk) +αδokφm

The weights of the hidden layers are updated using the learning rate αas:v _(nm) ←w _(nm) +αδhmαn

In one implementation, convolutional neural network 101 uses a gradientdescent optimization to compute the error across all the layers. In suchan optimization, for an input feature vector x and the predicted outputŷ, the loss function is defined as l for the cost of predicting ŷ whenthe target is y, i.e. l (ŷ, y). The predicted output ŷ is transformedfrom the input feature vector x using function ƒ. Function ƒ isparameterized by the weights of convolutional neural network 101, i.e.ŷ=ƒ_(w)(x). The loss function is described as l (ŷ, y)=l (ƒ_(w) (x), y),or Q (z, w)=l (ƒ_(w) (x), y) where z is an input and output data pair(x, y). The gradient descent optimization is performed by updating theweights according to:

$v_{t + 1} = {{\mu\; v_{t}} - {\alpha\frac{1}{n}{\sum\limits_{i = 1}^{N}\;{{\nabla w_{t}}{Q\left( {z_{t},w_{t}} \right)}}}}}$w_(t + 1) = w_(t) + v_(t + 1)

In the equations above, α is the learning rate. Also, the loss iscomputed as the average over a set of n data pairs. The computation isterminated when the learning rate α is small enough upon linearconvergence. In other implementations, the gradient is calculated usingonly selected data pairs fed to a Nesterov's accelerated gradient and anadaptive gradient to inject computation efficiency.

In one implementation, convolutional neural network 101 uses astochastic gradient descent (SGD) to calculate the cost function. A SGDapproximates the gradient with respect to the weights in the lossfunction by computing it from only one, randomized, data pair, z_(t),described as:v _(t+1) =μv−α∇wQ(z _(t) ,w _(t))w _(t+1) =w _(t) +v _(t+1)

In the equations above: α is the learning rate; μ s the momentum; and tis the current weight state before updating. The convergence speed ofSGD is approximately O(1/t) when the learning rate α are reduced bothfast and slow enough. In other implementations, convolutional neuralnetwork 101 uses different loss functions such as Euclidean loss andsoftmax loss. In a further implementation, an Adam stochastic optimizeris used by the convolutional neural network 101.

In one implementation, convolutional neural network 101 uses as inputtwo channels of stereoscopic or binocular images. In otherimplementations, it uses only a monocular image as input. In some otherimplementation, it uses a single two-dimensional (2D) image along withdepth information as the sole input channel. In yet anotherimplementation, it uses three input channels for a single image, suchthat the channels correspond to the red (R), blue (B) and green (G)components of the single image. In some implementations, the input imagedata 402 are pre-processed to generate one of, a combination of, or allof a grayscale map, a saliency map and a disparity map of the inputimage data 402, which substitute as the actual input image data 402 fedto convolutional neural network 101.

Convolution Layers

Convolution layers 104 of convolutional neural network 101 serve asfeature extractors. Convolution layers 104 act as adaptive featureextractors capable of learning and decomposing input image data 402 intohierarchical features. In one implementation, convolution layers 104take two images as input and produce a third image as output. In such animplementation, convolution operates on two images in two-dimension(2D), with one image being the input image and the other image, calledthe “kernel”, applied as a filter on the input image, producing anoutput image. Thus, for an input vector ƒ of length n and a kernel g oflength m, the convolution ƒ*g off and g is defined as:

${\left( {f*g} \right)(i)} = {\sum\limits_{j = 1}^{m}\;{{g(j)} \cdot {f\left( {i - j + {m/2}} \right)}}}$

The convolution operation includes sliding the kernel over the inputimage. For each position of the kernel, the overlapping values of thekernel and the input image are multiplied and the results are added. Thesum of products is the value of the output image at the point in theinput image where the kernel is centered. The resulting differentoutputs from many kernels are called feature maps.

Once the convolutional layers 104 are trained, they are applied toperform recognition tasks on new testing data 202. Since theconvolutional layers 104 learn from training data 102, they avoidexplicit feature extraction and implicitly learn from the training data102. Convolution layers 104 use convolution filter kernel weights, whichare determined and updated as part of the training process 400.Convolution layers 104 extract different features of a hand, which arecombined at higher layers. In one implementation, the convolutionfilters or kernels used by convolution layers 104 are hand-specific andextract relevant information from the input image data 402 and eliminateirrelevant variabilities. Some examples of global and local handfeatures extracted by the convolution layers 104 include oriented edges,end points, corners, lines and intersections.

Convolutional neural network 101 uses various number of convolutionlayers 104 ranging from one (1) to thirty-three (33), each withdifferent convolving parameters such as kernel size, strides, padding,number of feature maps and weights. In some implementations, only a setof convolution layers 104 are used instead of the all the convolutionallayers 104 to avoid overfitting and loss of generalization performance.

Sub-Sampling Layers

FIG. 6 is one implementation of sub-sampling layers 106 in accordancewith one implementation of the technology disclosed. Sub-sampling layers106 reduce the resolution of the features extracted by the convolutionlayers 104 to make the extracted features or feature maps 602 robustagainst noise and distortion. In one implementation, sub-sampling layers106 employ two types of pooling operations, average pooling 604 and maxpooling 606. The pooling operations divide the input intonon-overlapping two-dimensional spaces. For average pooling 604, theaverage of the four values in the region is calculated. For max pooling604, the maximum value of the four values is selected.

In one implementation, sub-sampling layers 106 include poolingoperations on a set of neurons in the previous layer by mapping itsoutput to only one of the inputs in max pooling 606 and by mapping itsoutput to the average of the input in average pooling 604. In maxpooling 606, the output of the pooling neuron is the maximum value thatresides within the input, as described by:φ₀=max(φ₁,φ₂, . . . ,φ_(N))

In equation above, N is the total number of elements within a neuronset.

In average pooling 604, the output of the pooling neuron is the averagevalue of the input values that reside with the input neuron set, asdescribed by:

$\varphi_{o} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\;\varphi_{n}}}$

In equation above, N is the total number of elements within input neuronset.

In FIG. 6 , the input is of size 4×4. For 2×2 sub-sampling, a 4×4 imageis divided into four non-overlapping matrices of size 2×2. For averagepooling 604, the average of the four values is the whole-integer output.For max pooling 606, the maximum value of the four values in the 2×2matrix is the whole-integer output.

Non-Linear Layers

FIG. 7 shows one implementation of non-linear layers 108 in accordancewith one implementation of the technology disclosed. Non-linear layers108 use different non-linear trigger functions to signal distinctidentification of likely features on each hidden layer. Non-linearlayers 108 use a variety of specific functions to implement thenon-linear triggering, including the rectified linear units (ReLUs),hyperbolic tangent, absolute of hyperbolic tangent, sigmoid andcontinuous trigger (non-linear) functions. In one implementation, a ReLUactivation implements the function y=max(x, 0) and keeps the input andoutput sizes of a layer the same. The advantage of using ReLU is thatconvolutional neural network 101 is trained many times faster. ReLU is anon-continuous, non-saturating activation function that is linear withrespect to the input if the input values are larger than zero and zerootherwise. Mathematically, a ReLU activation function is described as:

φ(h) = max (h, 0) ${\varphi(h)} = \left\{ \begin{matrix}{{h\mspace{14mu}{if}\mspace{14mu} h} > 0} \\{{0\mspace{14mu}{if}\mspace{14mu} h} \leq 0}\end{matrix} \right.$

In other implementations, convolutional neural network 101 uses a powerunit activation function, which is a continuous, non-saturating functiondescribed by:φ(h)=(a+bh)^(c)

In the equation above, a, b and c are parameters controlling the shift,scale and power respectively. The power activation function is able toyield x and y-antisymmetric activation if c is odd and y-symmetricactivation if c is even. In some implementations, the unit yields anon-rectified linear activation.

In yet other implementations, convolutional neural network 101 uses asigmoid unit activation function, which is a continuous, saturatingfunction described by the following logistic function:

${\varphi(h)} = \frac{1}{1 + e^{{- \beta}\; h}}$

In the equation above, β=1. The sigmoid unit activation function doesnot yield negative activation and is only antisymmetric with respect tothe y-axis.

Convolution Examples

FIG. 8 depicts one implementation of a two-layer convolution of theconvolution layers 104. In FIG. 8 , two input channels of 32×32stereoscopic (left and right) grayscale images are used, making theinput image data 402 of 2048 dimensions{[(32)×(32)=1024]+[(32)×(32)=1024]=2048}. At convolution 1, each of the32×32 grayscale images are convolved by a convolutional layer comprisingof two channels of sixteen kernels of size 3×3. The resulting sixteenfeature maps are then rectified by means of the ReLU activation functionat ReLU 1 and then pooled in Pool 1 by means of average pooling using asixteen channel pooling layer with kernels of size 3×3. At convolution2, the output of Pool 1 is then convolved by another convolutional layercomprising of sixteen channels of thirty kernels with a size of 3×3.This is followed by yet another ReLU2 and average pooling in Pool 2 witha kernel size of 2×2. Convolution layers 104 use varying number ofstrides and padding, for example, zero, one, two and three. Theresulting feature vector is five hundred and twelve (512) dimensions,according to one implementation.

In other implementations, convolutional neural network 101 usesdifferent numbers of convolution layers 104, sub-sampling layers 106,non-linear layers 108 and fully connected layers 118. In oneimplementation, convolutional neural network 101 is a shallow networkwith fewer layers and more neurons per layer, for example, one, two orthree fully connected layers with hundred (100) to two hundred (200)neurons per layer. In another implementation, convolutional neuralnetwork 101 is a deep network with more layers and fewer neurons perlayer, for example, five (5), six (6) or eight (8) fully connectedlayers with thirty (30) to fifty (50) neurons per layer. In yet anotherimplementation, convolutional neural network 101 is a multi-scalenetwork with three (3) scaled inputs representing depth data.

In another example, the input images are of different dimensions like96×96 and the preprocessing converts the input images into size 32×32. ACNN of seven layers includes an input layer, a convolution layer C1, asub-sampling layer S1, another convolution layer C2, anothersub-sampling layer S2, a hidden layer H and an output layer F.Convolution layer C1 uses six convolution kernels, each of size 5×5, toproduce six feature maps. Each feature map includes seven hundred andeighty four neurons {28×28=784}. At convolution layer C1, one hundredand fifty six parameters are trained {(6)×[(5)×(5)+(1)]=156}.Sub-sampling layer S1 also includes six feature maps, with each featuremap having one hundred and ninety six neurons {14×14=196}. Thesub-sampling window is a 2×2 matrix and since the sub-sampling step sizeis one, layer S1 includes five thousand eight hundred and eightyconnections {(6)×(196)×[(2)×(2)+(1)]=5880}. Every feature map in the S1layer includes a weight and bias, making the trained parameters twelve(12).

Convolution layer C2 includes sixteen feature maps and each feature mapincludes hundred neurons {{[(14)−(5)+(1)]×[(14)−(5)+(1)]=100} and adoptsa full connection. Each feature map of layer C2 has one hundred andfifty weights and a bias, making the trained parameters one hundred andfifty. Sub-sampling layer S2 includes sixteen feature maps. Each featuremap has twenty five neurons, making the total neurons in layer S2 fourhundred. The sub-sampling window is a 2×2 matrix, making the trainedparameters thirty two.

The hidden layer H includes one hundred and seventy neurons, each neuronconnected to four hundred neurons of layer S2. As a result, layer Hincludes forty eight thousand one hundred and twenty trained parameters.The output layer F includes eighty four neurons, making the trainedparameters fourteen thousand three hundred and sixty four{84×[(170)+(1)]=14364}.

Forward Pass

The output of a neuron of row x, column y in the l^(th) convolutionlayer and k^(th) feature map for ƒ number of convolution cores in afeature map is determined by the following equation:

$O_{x,y}^{({l,k})} = {\tanh\left( {{\sum\limits_{t = 0}^{f - 1}\;{\sum\limits_{r = 0}^{k_{h}}\;{\sum\limits_{c = 0}^{k_{w}}\;{W_{({r,c})}^{({k,t})}O_{({{x + r},{x + c}})}^{({{l - 1},t})}}}}} + {Bias}^{({l,k})}} \right)}$

The output of a neuron of row x, column y in the l^(th) sub-sample layerand k^(th) feature map is determined by the following equation:

$O_{x,y}^{({l,k})} = {\tanh\left( {{W^{(k)}{\sum\limits_{r = 0}^{S_{h}}\;{\sum\limits_{c = 0}^{S_{w}}\; O_{({{{x \times S_{h}} + r},{{y \times S_{w}} + c}})}^{({{l - 1},k})}}}} + {Bias}^{({l,k})}} \right)}$

The output of an i^(th) neuron of the l^(th) output layer is determinedby the following equation:

$O_{({l,i})} = {\tanh\left( {{\sum\limits_{j = 0}^{H}\;{O_{({{l - 1},j})}W_{({i,j})}^{l}}} + {Bias}^{({l,i})}} \right)}$Back Propagation

The output deviation of a k^(th) neuron in the output layer isdetermined by the following equation:d(O _(k) ^(o))=y _(k) −t _(k)

The input deviation of a k^(th) neuron in the output layer is determinedby the following equation:d(I _(k) ^(o))=(y _(k) −t _(k))φ′(v _(k))=φ′(v _(k))d(O _(k) ^(o))

The weight and bias variation of a k^(th) neuron in the output layer isdetermined by the following equation:ΔW _(k,x) ^(o))=d(I _(k) ^(o))y _(k,x)ΔBias_(k) ^(o))=d(I _(k) ^(o))

The output bias of a k^(th) neuron in the hidden layer is determined bythe following equation:

${d\left( O_{k}^{H} \right)} = {\sum\limits_{i = 0}^{i < 84}\;{{d\left( I_{i}^{o} \right)}W_{i,k}}}$

The input bias of a k^(th) neuron in the hidden layer is determined bythe following equation:d(I _(k) ^(H))=φ′(v _(k))d(O _(k) ^(H))

The weight and bias variation in row x, column y in an m^(th) featuremap of a prior layer receiving input from k neurons in the hidden layeris determined by the following equation:ΔW _(m,x,y) ^(H,k))=d(I _(k) ^(H))y _(x,y) ^(m)ΔBias_(k) ^(H))=d(I _(k) ^(H))

The output bias of row x, column y in an m^(th) feature map ofsub-sample layer S is determined by the following equation:

${d\left( O_{x,y}^{S,m} \right)} = {\sum\limits_{k}^{170}\;{{d\left( I_{m,x,y}^{H} \right)}W_{m,x,y}^{H,k}}}$

The input bias of row x, column y in an m^(th) feature map of sub-samplelayer S is determined by the following equation:d(I _(x,y) ^(S,m))=φ′(v _(k))d(O _(x,y) ^(S,m))

The weight and bias variation in row x, column y in an m^(th) featuremap of sub-sample layer S and convolution layer C is determined by thefollowing equation:

$\left. {{{\Delta\; W^{S,m}} = {\sum\limits_{x = 0}^{fh}\;{\sum\limits_{y = 0}^{fw}\;{{d\left( I_{{\lbrack{x/2}\rbrack},{\lbrack{y/2}\rbrack}}^{S,m} \right)}O_{x,y}^{C,m}}}}}{\Delta\;{Bias}^{S,m}}} \right) = {\sum\limits_{x = 0}^{fh}\;{\sum\limits_{y = 0}^{fw}\;{d\left( O_{x,y}^{S,m} \right)}}}$

The output bias of row x, column y in an k^(th) feature map ofconvolution layer C is determined by the following equation:d(O _(x,y) ^(C,k))=d(I _([x/2],[y/2]) ^(S,k))W ^(k)

The input bias of row x, column y in an k^(th) feature map ofconvolution layer C is determined by the following equation:d(I _(x,y) ^(C,k))=φ′(v _(k))d(O _(x,y) ^(C,k))

The weight and bias variation in row r, column c in an m^(th)convolution core of a k^(th) feature map of l^(th) convolution layer C:

$\left. {{{\Delta\; W_{r,c}^{k,m}} = {\sum\limits_{x = 0}^{fh}\;{\sum\limits_{y = 0}^{fw}\;{{d\left( I_{x,y}^{C,k} \right)}O_{{x + r},{y + c}}^{{l - 1},m}}}}}{\Delta\;{Bias}^{C,k}}} \right) = {\sum\limits_{x = 0}^{fh}\;{\sum\limits_{y = 0}^{fw}\;{d\left( I_{x,y}^{C,k} \right)}}}$

In one implementation, convolutional neural network 101 includes five(5) to seven (7) fully connected layers, each with hundred (100) to twohundred (200) neurons. In other implementations, convolutional neuralnetwork 101 includes any number of fully connected layers, each with anynumber of neurons. For instance, convolutional neural network 101includes three (3) fully connected layers with seven thousand onehundred eighty-eight neurons (7188) in the first and second layer andeighty-four (84) neurons in the output layer.

In regards to pre-processing 103, input image data 402 are pre-processedbefore they are fed into the convolutional neural network 101. In oneimplementation, the input image data 402 is made brightness, contrastand distance invariant to prevent the convolutional neural network 101from having to differentiate between darker and brighter hand images andin turn closer and farther hands. Normalizing the image brightness alsoreduces the number of parameters the convolutional neural network 101has to learn. Other examples of such pre-processing include noisereduction, color space conversion, image scaling and Gaussian pyramid.In one implementation, pre-processing 103 includes extracting regions ofinterest from the input image data 402, which include the hand. Theseregions of interest are referred to as “ImagePatches” and are used todetermine bounded hand places called “ImageRects.” In otherimplementations, techniques such as background subtraction, imagesegmentation and connected component labeling are used to extract theImagePatches. In one implementation, training data 102 is divided by thepalm width of the hand in order to make the units scale-invariant. Thisis useful because, during testing pipeline 200, the depth of a hand isdetermined based on its scale since a large object viewed from furtheraway looks mostly the same as a small object closer to the camera of thegesture recognition system. Thus, input image data 402 is fed to thefully connected layers or networks 118 as ImagePatches for furtherprocessing.

FIG. 9 illustrates real images 900 of two sets of sixteen (16) 3×3convolution kernels learned and used for feature extraction fromstereoscopic images. FIG. 10 illustrates a real image 1000 of theresulting feature map produced by the convolution kernels shown in FIG.9 . Real image 1000 is the convolved result of the image pair which, inone implementation, is fed to the fully connected layers or networks118. Real image 1000 includes sixteen (16) sub-images that representdifferent features of the hand pose identified and extracted by theconvolution kernels shown in FIG. 9 . FIG. 11 illustrates how thelearned convolution kernels applied locally 1100 to an input image (onthe left) produce a convolved image (on the right) that is robust to thebackground and the clutter, i.e., ignores the background and the clutterand only extracts the hand features.

In another implementation, global features of the hand are extractedusing a principal component analysis (PCA) or Karhunen-Loevetransformation technique, illustrated in FIG. 12 . PCA exploits thecovariance of pixel values to reduce the dimensionality of the inputimage data while retraining the majority of variation present in theimage. A real image of an example PCA basis 1200 for an open-hand poseis shown in FIG. 12 . In FIG. 12 , a one thousand and twenty-four[(32)×(32)=1024] dimensional image was reduced to sixty-four (64) mostdominant dimensions using the PCA technique. As depicted in FIG. 12 ,the sixty-four (64) most dominant dimensions include more discernablepatterns and correlations of the hand. Therefore, data reductiontechniques like PCA and convolution greatly improve the trackingperformance by transforming the input into a space that is moreconducive for learning of the fully connected layers or networks 118.

Fully Connected Layers or Networks

In a fully connected layer of a neural network, all the elements of allthe features of the previous layer get used in the calculation of eachelement of each output feature. Convolutional neural network 101includes fully connected layers or networks 118 that are comprised oftwo types of neural networks: “master” or “generalists” networks 110 and“expert” or “specialists” networks 112. Both, master networks 110 andexpert networks 112, are fully connected neural networks that take afeature vector of an input hand image and produce a prediction of thehand pose. Both, master networks 110 and expert networks 112,respectively include eight (8) to twelve (12) fully connected layers andeach of these fully connected layers has between hundred (100) to twohundred (200) neurons. In one implementation, an exponential linear unit(ELU) activation function is used by the master networks 110 and expertnetworks 112. In another implementation, a rectified linear unit (ReLU)activation function is used by the master networks 110 and expertnetworks 112. In yet another implementation, a leaky rectified linearunit (LReLU) activation function is used by the master networks 110 andexpert networks 112. In some implementations, ELU activation functionimproves the learning of master networks 110 and expert networks 112better compared to other activation functions. More information aboutELU activation function can be obtained from Djork-Arné Clevert, ThomasUnterthiner and Sepp Hochreiter, Fast and Accurate Deep Network Learningby Exponential Linear Units (ELUs), Version v5, Feb. 22, 2016,accessible at http://arxiv.org/abs/1511.07289, which is incorporatedherein in its entirety. Furthermore, within each of the master networks110 and expert networks 112, there are two kinds of neural networks:“temporal” networks and “atemporal” networks, as discussed supra.

FIG. 13 illustrates one implementation of a fully connected masternetwork 110 or a fully connected expert network 112. Fully connectedneural network 1300 includes twelve (12) layers (L), L1 to L12, and eachof the layers L1 to L2 includes between hundred (100) and two hundred(200) neurons. Furthermore, the last layer L12 includes eighty-four (84)output neurons that produce 84 (28×3) estimates for 3D joint locationsof twenty-eight (28) hand joints illustrated in FIGS. 5A and 5B. Thus,the final layer of every master network 110 and every expert network112, irrespective of the total number of layers, includes 84 outputneurons estimating the 28 hand joint locations in 3D space.

Master networks 110 and expert networks 112 differ from each other basedon the data on which they are trained. In particular, master networks110 are trained on the entire data set. In contrast, expert networks 112are trained only on a subset of the entire dataset. In regards to thehand poses, master networks 110 are trained on the input image datarepresenting all available hand poses comprising the training data 102(including both real and simulated hand images). Expert networks 112 areindividually trained on specific classes of hand poses such as open-handposes, first poses, grab poses, V-shaped poses or pinch poses. Thisdistinction allows convolutional neural network 101 to have“generalists” in the form of master networks 110 that are trained overthe entire available training data 102, which nearly cover the space ofall possible poses and hence generalize better over unseen hand poses(not present in the training data 102). For example, when convolutionalneural network 101 receives testing data 202 on which it has never beentrained, it invokes the master networks 110 to get a rough pose estimateof the unseen hand image. In addition to the generalists, convolutionalneural network 101 also has “specialists” in the form of expert networks112 that are trained only on specific pose-types. These specialistsallow convolutional neural network 101 to generate accurate hand poseestimates for the unseen hand image once the master networks 110 haveroughly predicted which pose-type the unseen hand image best correspondsto. In one example, one or more master networks 110 predict that aparticular hand image corresponds to a curled-finger pose. Convolutionalneural network 101 uses this rough estimate to invoke three (3) expertnetworks 112 that have been only trained on curled-finger-type posessuch as pinch poses, grab poses and punch poses (all with curled-infingers and thumb). Then, the expert networks 112 accurately predict notonly whether the particular hand image is a pinch pose, a grab pose or apunch pose, but also what kind of pinch pose, grab pose or punch posethe particular hand image is, for example, a leftward/rightward/centeredpinch pose, leftward/rightward/centered grab pose orleftward/rightward/centered punch pose.

According to one implementation, the master networks 110 and expertnetworks 112 serve as “regressors” for the convolutional neural network101. In such an implementation, the outputs of the master networks 110and expert networks 112 are not in the form of pose class names like apinch pose, a grab pose or a punch pose. Instead, the master networks110 and expert networks 112 generate, as output, estimates of “handposition parameters.” These hand position parameters are in the form ofjoint location models, joint angel models, capsule models, skeletonmodels, volumetric models and/or mesh models, muscle hand models, eachin 2D and/or 3D space. In other implementations, the master networks 110and expert networks 112 serve as “classifiers” for the convolutionalneural network 101 and classify an input hand images into one or morepose classes like leftward/rightward/centered pinch pose,leftward/rightward/centered grab pose or and leftward/rightward/centeredpunch pose.

Master or Generalists Networks

As discussed infra, master or generalists networks 110 are fullyconnected neural networks that are trained over the entire availabletraining data 102 of hundred thousand (100,000) and one billion(1,000,000,000) hand images to generate rough hand poses estimates. Inone implementation, training data 102 is split into training data 102and validation data. This validation data is carved out of the trainingdata 102 in order to test the generalization performance of theconvolutional neural network 101 by feeding it hand images on which ithas not been trained. Based on the cross-validation performance of theconvolutional neural network 101 on the validation data, differenthyper-parameters of the convolutional neural network 101 are tuned. Someexamples of these hyper-parameters include learning rate, batch size forthe gradient descent solver, pooling windows, strides, padding,convolutional kernels, momentum, number of layers, number of neurons perlayer, and others.

In some implementations, the training data 102 is split into a 90:10split proportion such that ninety (90) percent of the training data 102is retained and ten (10) percent of the training data 102 is used asvalidation data. In other implementations, the split proportions areconfigured to different ratios. Convolutional neural network 101initiates these splits randomly such that different combinations of thehundred thousand (100,000) to one billion (1,000,000,000) hand imagesare bucketed as training data 102 or validation data on every split.Thus, since the composition of the training data 102 changes randomlyfrom one split to the next, different versions of the training data 102comprising of different images are used to train the master networks110. This results in the convolutional neural network 101 havingmultiple master networks 110 that are trained on different versions oftraining data 102. FIG. 14 depicts one implementation of three (3)master networks that are trained on different versions 1400 of trainingdata 102 created by the validation data split. In FIG. 14 , the circlesrepresent the entire training data 102 before validation data(dark-grey) is carved out of it to produce a diminished composition ofthe training data 102 (off-white). In each of the circles, a differentportion of the training data 102 makes up the validation data and thediminished training 102, thus creating different versions of thetraining data 102. Each of the different versions of the training data102 are used train separate ones of the master networks 110 such as thefirst, second and third master networks shown in FIG. 14 . Furthermore,the training hyper-parameters are also varied between the differentmaster networks 110. Consequently, the master networks 110 are able togeneralize better because they cover unique varieties of hand images andproduce as outputs different rough pose estimates for the same inputhand image.

Convolutional neural network 101 comprises of twenty (20) to hundred(100) master networks 110. In one implementation, the number of splitsor master networks 110 is tunable. As a result, the number of masternetworks 110 in convolutional neural network 101 is configurable basedon the available computation resources and the computation platform. Inone implementation, one (1) to three (3) master networks 110 are usedfor a mobile device application. In another implementation, three (3) tofive (5) master networks 110 are used for a head-mounted displayapplication. In yet another implementation, five (5) to eight (8) masternetworks 110 are used for a personal computer (PC) or laptopapplication. In a further implementation, eight (8) to twelve (12)master networks 110 are used for an automobile application.

Expert or Specialists Networks

As discussed infra, expert or specialist networks 112 are fullyconnected neural networks that are trained over a subset of trainingdata 102 corresponding to specific pose-types. This concept isillustrated in FIG. 15 . For clarity's sake, FIG. 15 characterize theexpert networks 112 as classifiers that classify the output hand poseestimates into one or more pose classes. Such a characterization is madeonly to distinguish between the master networks 110 and the expertnetworks 112. In other implementations, the master networks 110 andexpert networks 112 are not classifiers, but instead regressors thatgenerate 84 (28×3) estimates for 3D joint locations of twenty-eight (28)hand joints illustrated in FIGS. 5A and 5B. In FIG. 15 , circle 1500represents the entire available training data 102 of hundred thousand(100,000) and one billion (1,000,000,000) hand images (including bothreal and simulated hand images). Circle 1500 is further partitioned intoclusters using eleven (11) arches. Each of these eleven (11) archesrepresents a separate pose-type (P), P1 to P11. Furthermore, each of thepose-type (P) overlaps to some degree with one or more other pose types(Ps). In circle 1500, each pose-type (P) (e.g., pinch pose, first pose,flat-hand pose) represents a separate expert network 112, as illustratedin the pose-to-expert network mapping shown in FIG. 15 . Thus, theoverlapped spaces like “P5, P4, P3” in circle 1500 representintersection of one or more similar poses (e.g., loose-pinch pose,loose-tilted-fist pose, loose-tilted-grab pose) on which multiple expertnetworks are trained. In one implementation, the pose-types (Ps) aremapped in memory to their corresponding input hand images. Thus,according to one implementation, each of the expert networks 112 aretrained on at least three (3) pose-types and the numerous variantsassociated with each of the three (3) pose-types. In anotherimplementation, each of the expert networks 112 are trained on at leastfive (5) pose-types and the numerous variants associated with each ofthe five (5) pose-types. In yet another implementation, each of theexpert networks 112 are trained on at least eight (8) pose-types and thenumerous variants associated with each of the eight (8) pose-types. Theoverlapping between the expert networks 112 prevents them from beingover-trained from a particular pose-type and allows them to generalizeover multiple pose-types. The overlap also prevents discontinuity andharsh cut-offs between the expert networks 112. As a result, multipleexpert networks 112 that have been trained on similar input images areinvoked for each input hand image so as to get multiple estimates forthe hand position parameters. Thus, for every input hand image, at leastthree (3) expert networks 112 are invoked and three (3) accurateestimates of hand position parameters are computed. In anotherimplementation, for every input hand image, at least five (5) expertnetworks 112 are invoked and five (5) accurate estimates of handposition parameters are computed. In yet another implementation, forevery input hand image, at least eight (8) expert networks 112 areinvoked and eight (8) accurate estimates of hand position parameters arecomputed. Furthermore, training the expert networks 112 on focused imagetypes makes them more robust to specific poses, different backgroundsand hand shapes.

Convolutional neural network 101 comprises of fifty (50) to two hundred(200) expert networks 112, according to one implementation. In oneimplementation, the number of partitions or expert networks 112 istunable. As a result, the number of expert networks 112 in convolutionalneural network 101 is configurable based on the available computationresources and the computation platform. In one implementation, three (3)to five (5) expert networks 112 are used for a mobile deviceapplication. In another implementation, five (5) to ten (10) expertnetworks 112 are used for a head-mounted display application. In yetanother implementation, eight (8) to twelve (12) expert networks 112 areused for a personal computer (PC) or laptop application. In a furtherimplementation, fifty (50) to two hundred (200) expert networks 112 areused for an automobile application. Furthermore, the expert networks 112are configurable based on the specificity of a particular pose-type onwhich they are trained. For example, a given expert network 112 istrained on all pinch poses, according to one implementation. In anotherimplementation, it is trained only on vertical-pinch poses and not onhorizontal-pinch poses. In other implementations, the amount of overlapbetween the expert networks 112 is also configurable such that aspecification is set on how many and which different pose-types are usedto train a particular expert network 112.

Synergy Between Master and Expert Networks During Testing

In one implementation, the hand position parameters predicted by boththe master networks 110 and expert networks 112 are used to generate thefinal hand pose estimation. In such an implementation, thedimensionality-reduced feature vector (e.g., 512 dimensions), receivedfrom the convolution layers 104, sub-sampling layers 106 and non-linearlayers 108, is provided to multiple master networks 110 during testingpipeline 200. FIG. 16 illustrates one implementation of synergy 1600between the master networks 110 and expert networks 112 during testing200. In the example shown in FIG. 16 , the feature vector is provided tothree separate fully-connected master networks 110. Each of the masternetworks 110 generates rough hand position parameters (e.g., 84 (28×3)estimates for 3D joint locations of twenty-eight (28) hand joints). Eachof these rough hand position parameters are used to invoke separate setsof expert networks 112 that are respectively similar to thecorresponding master networks 110. In the example shown in FIG. 16 ,three (3) expert networks 112 are invoked for each of the three (3)expert networks 112. Once the nine (9) expert networks 112 areidentified, the dimensionality-reduced feature vector (e.g., 512dimensions) initially provided to the master networks 110, is provide tothe nine (9) expert networks 112 to generate nine (9) different accurateestimates of the hand position parameters (e.g., 84 (28×3) estimates for3D joint locations of twenty-eight (28) hand joints). In yet anotherimplementation, some of the master networks 110 serve as classifiersthat first determine whether the input image is of a hand or not. Insuch an implementation, the determination made by a hand-classifiermaster network 110 about a feature vector's similarity to a hand shapeis used prior to invoking other master networks 110 and/or expertnetworks 112.

FIG. 17 illustrates one implementation of a pose space 1700 of trainingdata 102 in an eighty-four (d1-d84) dimensional coordinate systemrepresenting eighty-four (84) dimensional hand poses comprised oftwenty-eight (28) 3D (x₀, y₀, z₀) hand joints. In pose space 1700, eachpoint represents a single eighty-four (84) dimensional hand posecomprised of twenty-eight (28) 3D (x₀, y₀, z₀) hand joints. In otherimplementations, pose space 1700 is based on other hand positionparameters such as joint angles, segment lengths, wrist length, palmlength, and the like. As shown in FIG. 17 , there is significant overlapbetween the pose-points to represent similarity between thecorresponding hand poses. In one implementation, the poses or pose-typesrepresented by the pose-points are mapped in memory to theircorresponding input hand images.

Master experts 110 are trained on one or more versions of training data102 represented by pose-points depicted in pose space 1700 determined bywhich portion of training data 102 is used as validation data. Incontrast, expert networks 112 are trained on specific poses orpose-types in the pose space 1700. The different poses or pose-types aredifferentiated or partitioned in pose space 1700 using one or moresegmentation models, including but not limited to k-means, overlappingk-means, kx-trees, density estimation, k-nearest neighbors, Kohonen net,self-organizing maps modeling (SOM), adaptive resonance theory models(ART), as well as other feature extraction techniques. In otherimplementations, a variety of clustering techniques are applied to thepose space 1700, such as unsupervised clustering techniques, where thetask is to develop classification and sorting of the poses or pose-typeswithout regards to a predefined number of groups or clusters to begenerated. Such unsupervised clustering techniques seek to identifysimilarities between portions of the poses or pose-types within the posespace 1700 in order to determine whether the poses or pose-types arecharacterized as forming a cluster. Furthermore, the similarity betweenposes or pose-types is based on one or more hand position parameterslike hand sub-elements position such as fingers, device position, devicerotation, device viewpoint, background, hand position, occlusion, pitch,yaw, roll, path, trajectory, joint locations, joint angles, palmposition, palm orientation, finger segment length, wrist positions,wrist orientation, curling, stubbiness, translation, rotation, and otherparameters discussed infra. In other implementations, the number ofclusters in configurable by a human.

FIG. 18 illustrates one implementation of a clustered pose space 1800.As shown in FIG. 18 , each pose or pose-type in pose space 1800 isclustered in at least one cluster. In other implementations, each poseor pose-type in pose space 1800 is clustered in multiple clusters suchas two, three, five, eight and so on. Also shown in FIG. 18 is that eachpose cluster is represented by a centroid, depicted with an “X” (white)in each cluster of pose space 1800. The centroid represents the bestcandidate pose for a given set of poses or pose-types grouped in a posecluster. For example, if a pose cluster includes loose-pinch poses,loose-tilted-fist poses, loose-tilted-grab poses, the representativecentroid pose (X) is a curled-finger-closed-hand pose, in oneimplementation, or a pinch, first or grab pose in anotherimplementation.

Specifically, each of the expert networks 112 are trained on a differentpose cluster shown in pose space 1800. In the example shown in FIG. 18 ,there are thirty-five (35) pose-clusters. This means thirty-five (35)separate expert networks 112 are trained. Also, as discussed supra,there are significant overlaps between the clusters so that each of theexpert networks 112 are trained on multiple pose or pose-types. In otherwords, input hand images corresponding to a give pose or pose-type arefed to multiple expert networks 112. This is done to prevent the expertnetworks 112 from becoming too focused on a given pose or pose-type andnot be able to generalize. As well, this overlapping between poseclusters allows convolutional neural network 101 to invoke multipleexpert networks 112 for a single input hand image, and thus generatemultiple pose estimates, which are in turn used for final poseestimation, as discussed supra.

FIG. 19 shows one implementation of synergy between master networks 110and expert networks 112 in pose space 1900. As, discussed supra, one ormore master networks 110 processes a dimensionally-reduced featurevector to generate rough estimates of hand position parameters. Inrepresentative FIG. 19 , these rough estimates are depicted as differenttriangles. So, in the example used in FIG. 19 , three (3) masternetworks 110 have estimated that an input feature vector produces anoutput hand pose located at the triangles in pose space 1900. In otherimplementations, more or less pose estimates are received from fewer orgreater number of master networks 110. Advancing further, each of themaster pose estimates 1, 2 and 3, invokes one or more representativecentroid poses (X) that is nearest to it. The proximity between a givenmaster pose estimate and representative centroid poses (X) of differentpose clusters in the pose space 1900 is determined using a variety ofdistance measures, such as Euclidean distance, standardized Euclideandistance, weighted Euclidean distance, squared Euclidean distance,Manhattan distance, Minkowski distance, Mahalanobis distance, orChi-square distance. Further, the number of proximate representativecentroid poses (X) to select is configurable such that one, two or threeof the nearest pose clusters are selected based on their correspondingrepresentative centroid poses (X).

Moving ahead, the purpose of selecting multiple representative centroidposes (X) proximate to a given master pose estimate is to identify whichpose cluster and its poses or pose-types are most similar to the givenmaster pose estimate. Once one or more nearby pose clusters areidentified for a given master pose estimate, the corresponding expertnetworks 112 that are trained on the identified pose clusters areinvoked to generate their respective pose estimates. Thin invocationincludes feeding to the invoked expert networks 112, the originalfeature vector used by the one or more master networks 110 to generatethe master pose estimates 1, 2 and 3. In the example shown in FIG. 19 ,three (3) pose nearby poses clusters are identified for each of themaster pose estimates 1, 2 and 3 based on respective distances D1, D2,D3, D4, D5, D6, D7, D8 and D9. This results in identification of nine(9) expert networks 112 that are now used to generate nine (9) newexpert pose estimates in addition to the three (3) master pose estimates1, 2 and 3. As shown in FIG. 16 , the new expert pose estimates aregenerated by feeding the dimensionally-reduced feature vector to theidentified expert poses 112. In one example, the master pose estimatesrepresent a pinch pose. Then, multiple nearby pose clusters relating toa pinch pose, such as a leftward-pinch pose, a rightward-pinch pose, afull-finger pinch pose, etc. are selected so that the correspondingexpert networks 112 generate the accurate and precise hand poseestimates that represent the exact hand pose of the input hand images.

The following section discusses how the master pose estimates and theexpert pose estimates are used to generate a final pose estimate.

In one implementation, the master pose estimates are rough estimates ofhand position parameters that are used to generate accurate and preciseestimates of the hand position parameters using the expert networks 112.In other implementations, the master pose estimates themselves areaccurate estimates of hand position parameters and are used directly forthe final hand pose estimation without reliance on the expert networks112. Such a “master-only” implementation is used during testing 200under so-called “high-confidence” scenarios to generate initial handpose estimates. Such an implementation is depicted in FIGS. 1 and 2 bythe alternative arrows directly from the master networks 110 to the handpose estimation 114.

FIG. 20 shows a representative method 2000 of synergy between atemporalmaster networks 110 and atemporal expert networks 112 in accordance withone implementation of the technology disclosed. Flowchart 2000 can beimplemented at least partially with a computer or other data processingsystem, e.g., by one or more processors configured to receive orretrieve information, process the information, store results, andtransmit the results. Other implementations may perform the actions indifferent orders and/or with different, fewer or additional actions thanthose illustrated in FIG. 20 . Multiple actions can be combined in someimplementations. For convenience, this flowchart is described withreference to the system that carries out a method. The system is notnecessarily part of the method.

At action 2002, a first set of atemporal generalist neural networks aretrained using simulated hand position images, as discussed infra.

At action 2004, the simulated hand position mages are subdivided intooverlapping specialist categories, as discussed infra.

At action 2006, a first set of atemporal specialist neural networks aretrained using the specialist categories of the simulated hand positionimages, as discussed infra.

At action 2008, during testing, a first set of estimates of handposition parameters are received from the atemporal generalist neuralnetworks, as discussed infra.

At action 2010, during testing, a second set of atemporal specialistneural networks are identified based on the first set of estimates ofhand position parameters provided by the atemporal generalist neuralnetworks, as discussed infra.

At action 2012, during testing, a second set of estimates of handposition parameters are received from the identified atemporalspecialist neural networks, as discussed infra.

At action 2014, during testing, a final set of estimates of handposition parameters is determined based on the first and second set ofestimates, as discussed infra.

Temporal Networks

Master networks 110 and expert networks 112 are further divided into twoclasses of neural networks: atemporal neural networks and temporalneural networks. The neural networks discussed supra are mostlyatemporal neural networks. This section discusses temporal neuralnetworks. Like atemporal neural networks, temporal neural networks arealso fully connected layers or networks. In one implementation, temporalneural networks are trained separately from the atemporal neuralnetworks during training 100. This is done because the input to thetemporal neural networks differs from the input to the atemporal neuralnetworks.

Temporal neural networks are used for learning gesture sequences andpredicting the next pose in the subsequent frame based on the prior posein the previous frame. In one implementation, temporal neural networksmemorize the past poses for given hand that has entered the field ofview of a gesture recognition system. Further, the temporal neuralnetworks include feedback loops that produce recurrent connectionsbetween the neurons of the temporal neural networks. In oneimplementation, the temporal neural networks are trained on sequentialinputs to produce sequential outputs that are mapped and synchronizedbased on their time-variance. In some implementations, temporal neuralnetworks are recurrent neural networks (RNNs) based on long short termmemory (LSTM). In another implementation, temporal networks arebidirectional recurrent neural networks (BRNNs) based on long short termmemory (LSTM) that maintain gesture sequences in forwards and backwardsformat in separate hidden layers.

At training 100, temporal neural network are trained using a combinationof two feature vectors. The first feature vector is the 512-dimensionalfeature convolved from the convolution layers 102, as discussed infra.The second feature vector represents the 84-dimensional prior poseestimate determined by the temporal master networks 110 and temporalexpert networks 112. Thus, in one implementation, atemporal master andexpert networks differ from the temporal master and expert networks inthe sense that the former is trained on the current 512-dimensionalfeature vector extracted from the current image and the latter istrained on a 596-dimensional feature vector [(512)+(84)=596] composed ofthe current image (512D) and the prior estimate pose (84D). Thecombination of the current feature vector and the prior pose featurevector allows the temporal neural networks to learn ambiguous posesduring training 100 and resolve them during training 200. For example,when the input hand image represents a vertical hand from the point ofview of the gesture recognition system, convolutional neural network 101may not be able to differentiate between a supine hand (front-facing) ora prone hand (back-facing). In such circumstances, convolutional neuralnetwork 101 uses temporal master networks 110 and temporal expertnetworks 112 to resolve the ambiguity by using the prior poseestimation. So, continuing the supine and prone example, if the priorpose was a supine pose, then temporal master networks 110 and temporalexpert networks 112 produce a vertical supine pose. On the other hand,if the prior pose was a prone pose, then temporal master networks 110and temporal expert networks 112 produce a vertical prone pose. Theseresults are consistent with the natural motions of a human hand and theconstraints of the hand anatomy because the gesture recognition systemdisclosed herein captures between hundred (100) and three hundred (300)frames per second and it is very unlikely that a human hand traversesfrom a supine pose to a prone pose within hundredth or three hundredthof a second. Other examples of ambiguous poses include different handposes that have similar input hand images, highly occluded poses,ambiguously rotated poses, and others.

In one implementation, the temporal master networks 110 and temporalexpert networks 112 are Jordan or Elman networks that are trained usinga regularization technique shown in FIG. 21 . According toregularization 2100, during time t₀ of training 100, the input fed tothe temporal master networks 110 and temporal expert networks 112 iscontaminated with noise (e.g., extra 84 dimensions) that serves as abias. In this implementation, the noise or the extra dimensions of theextra feature vector are not from the prior pose but instead randomlygenerated. This is done to prevent the temporal master networks 110 andtemporal expert networks 112 from giving unnecessary weight to the priorpose and generating an over-fitted output that matches the prior pose.Using the randomly generated noise during training 100 allows thetemporal master networks 110 and temporal expert networks 112 to giveadequate weight to the current input image during testing 200. However,during testing 200, the extra information is not noise, but instead thefeature vector representing the 84D prior pose and previous frame. Asillustrated in FIG. 22 , at time t₁ of testing 200, temporal neuralnetworks 2200 store the prior pose estimate 1 calculated from featurevector 1 extracted from input hand images 1. At time t₂ of testing 200,temporal neural networks 2200 combine the prior pose estimate 1 with thecurrent feature vector 2 extracted from the current input hand images 2and generate the new pose estimate 2.

In other implementations, temporal neural networks store the poseinformation across multiple frames and time variances. As discussedsupra, simulator 4100 generates simulated gesture sequences anddedicated sequences that mimic realistic and most common hand gesturesand motions. These simulated gesture sequences allow the temporal neuralnetworks to train and learn on a series of hand poses during training100 that represent the series of hand poses received during testing 200.As a result, during testing 200, temporal neural networks maintain amemory of a series of hand poses across many frames and time variances.Further, these stored hand poses are used in the predicting of a currenthand pose. During instances of ambiguous poses, temporal neuralnetworks, being trained on simulated gesture sequences and dedicatedsequences that represent realistic and most common hand gestures andmotions, know what the next temporally likely pose estimation should be.Thus, pose estimates that are beyond a threshold of the next temporallylikely pose estimation or contradict the next temporally likely poseestimation are discarded in favor of more consistent pose estimations.As illustrated in FIG. 23 , temporal master and expert neural networks2300 use a sequence of temporally varied t₁ to t₅ frames 1 to 4 andtheir corresponding poses estimates 1 to 4 to generate a current poseestimate 5 at time t₅ based on the current feature vector 5 extractedfrom the current hand images 5.

In some implementations, temporal master and expert neural networkssynergize analogous to the temporal master and expert neural networks.

FIG. 24 shows a representative method 2400 of synergy between temporalmaster networks 110 and temporal expert networks 112 in accordance withone implementation of the technology disclosed. Flowchart 2400 can beimplemented at least partially with a computer or other data processingsystem, e.g., by one or more processors configured to receive orretrieve information, process the information, store results, andtransmit the results. Other implementations may perform the actions indifferent orders and/or with different, fewer or additional actions thanthose illustrated in FIG. 24 . Multiple actions can be combined in someimplementations. For convenience, this flowchart is described withreference to the system that carries out a method. The system is notnecessarily part of the method.

At action 2402, a first set of temporal generalist neural networks aretrained using a current set of simulated hand position images and one ormore prior pose estimates temporally linked as a gesture sequence and/orrandomly generated image data, as discussed infra. In oneimplementation, the randomly generated image data is used as noise.

At action 2404, a dataset of simulated hand position images issubdivided into overlapping specialist categories, as discussed infra.

At action 2406, a first set of temporal specialist neural networks aretrained using the specialist categories of the simulated hand positionimages and corresponding one or more prior pose estimates in thespecialist categories temporally linked as a gesture sequence, asdiscussed infra.

At action 2408, during testing, a first set of estimates of handposition parameters are received from the temporal generalist neuralnetworks based on at least one real hand position image and one or moreprior pose estimates made during the testing, as discussed infra.

At action 2410, during testing, a second set of temporal specialistneural networks are identified based on the first set of estimates ofhand position parameters provided by the generalist neural networks, asdiscussed infra.

At action 2412, during testing, a second set of estimates of handposition parameters are received from the identified temporal specialistneural networks, as discussed infra.

At action 2414, during testing, a final set of estimates of handposition parameters is determined based on the first and second set ofestimates, as discussed infra.

Hand Pose Estimation

As discussed infra, each of the master networks 110 and expert networks112 produce as output 84 (28×3) estimates for 3D joint locations oftwenty-eight (28) hand joints. The technology disclosed performs handpose estimation 114 on a so-called “joint-by-joint” basis. So, when aplurality of estimates for the 28 hand joints are received from aplurality of expert networks 112 (and from master experts 110 in somehigh-confidence scenarios), the estimates are analyzed at a joint leveland a final location for each joint is calculated based on the pluralityof estimates for a particular joint. This is a novel solution discoveredby the technology disclosed because nothing in the field of artdetermines hand pose estimates at such granularity and precision.Regarding granularity and precision, because hand pose estimates arecomputed on a joint-by-joint basis, this allows the technology disclosedto detect in real time even the minutest and most subtle hand movements,such a bend/yaw/tilt/roll of a segment of a finger or a tilt an occludedfinger, as demonstrated supra in the Experimental Results section ofthis application.

Outlier-Robust Covariance Propagation

For a single joint, each set of joint location estimates produced bymultiple expert networks 112 maintains an outlier-robust covariance thatis updated every tracking frame. For instance, for an individual jointthat has twelve (12) incoming estimates from the expert networks 112(and from master experts 110 in some high-confidence scenarios), theestimates are combined together using a covariance distribution. Oncethe covariance distribution is calculated for a prior frame, Mahalanobisdistances of the new incoming estimates in the current frame aredetermined, according to one implementation. In other implementations,other distance measures such as projection statistics and Euclideandistances are used. The distances are determined from the covariancedistribution calculated in the prior frame. The distances are thenconverted into probabilities (e.g., using a Gaussian probabilitydistribution or Chi-square p-values). These probabilities are then usedas weights to compute the new covariance distribution of all the newpoints for the current frame. This way, the estimates that are furtherfrom the prior covariance distribution are detected as outliers andgiven very low weights and are ignored. In contrast, the inliers aregiven high weights and contribute more to the updated covariancedistribution of the current frame. In one implementation, to preventsingularities, a regularization factor is used which extends thecovariance and prevents the covariance from becoming dedicated to alocal minima in the fast moving gestures like rapid grabbing andreleasing motions.

As discussed infra, for each individual joint, an outlier-robustestimate of the mean and covariance of estimate distributions iscalculated based on a weighted form of the mean and covariance, wherethe weights depend on probabilities formed in the course of an outlieridentification scheme. First, a multivariate Gaussian covariance of 3Djoint location estimates for each of the individual joints of the 28hand joints is calculated separately and simultaneously. For a singlejoint J, E joint location estimates are received from E expert networks112 across F frames. Also, x_((j)) ^((ƒ)), y_((j)) ^((ƒ)) and z_((j))^((ƒ)) represent the x, y and z coordinates of the j^(th) joint at frameƒ. Further, sequence vector V represents the E joint location estimatesreceived from E expert networks 112, mathematically represented asV=[x₁, . . . , x_(E), y₁, . . . , y_(E), z₁, . . . , z_(E)]′. Thus, thesample covariance matrix for the sequence vector V is described as:

${{COV}(V)} = {\frac{1}{F - 1}{\sum\limits_{f = 1}^{F}\;{\left( {V - \overset{\_}{V}} \right)\left( {V - \overset{\_}{V}} \right)^{\prime}}}}$

In the equation above, V is the sample mean of V and ′ is the transposeoperator (T).

In one implementation, a Mahalanobis distance outlier rejection schemeis used. Mahalanobis distance is a distance measure based on theweighted Euclidean norm of the separation between a possible outlier andthe sample mean, which takes into account the sample covariance matrix.Thus, for m points in an n-dimensional multivariate sample representedby the vectors x_(i) (i=1, . . . , m), the outlier rejection schemebased on Mahalanobis distances is defined using:

MD_(i) = ((x_(i) − μ)^(T)COV⁻¹(x_(i) − μ))^(1/2)  for  i = 1, …  , n$\mu = {\frac{1}{m}{\sum\limits_{i = 1}^{m}\; x_{i}}}$MD_(i) = ((x_(i) − t)^(T)C⁻¹(x_(i) − t))^(1/2)  for  i = 1, …  , n${COV} = {\frac{1}{m - 1}{\sum\limits_{i = 1}^{m}\;{\left( {x_{i} - \overset{\_}{\mu}} \right)\left( {x_{i} - \overset{\_}{\mu}} \right)^{\prime}}}}$

In the equations above, μ is the estimated multivariate arithmetic meanand COV is the estimated covariance matrix or sample covariance matrix.In some implementations, for multivariate normally distributed data, thevalues are approximately Chi-square distributed with n degrees offreedom (χ_(n) ²). Multivariate outliers are then defined asobservations having a large (squared) Mahalanobis distance. In oneimplementation, the Mahalanobis Distances represent the surface of ann-dimensional ellipsoid centered at the sample mean. The square of theMahalanobis distances follow a χ² distribution with n degrees of freedomfor Gaussian input data.

In another implementation, a weighted robust Kalman filter operation isperformed on the 3D joint location estimates for individual joints ofthe 28 hand joints. In such an implementation, the outliers in the 3Djoint location estimates are determined by thresholding the propagatedcovariance using a Kalman gain matrix based on the Mahalanobis distance.If the Mahalanobis distance is less than a certain threshold value, thenit is considered an inlier and processed. Otherwise, it is an outlierand ignored. Therefore, an outlier rejection scheme based on a Kalmanfilter considers all points satisfying to be outliers as:MD _(i)=(χ_(n,α) ²)

In the equation above, α is the probability that a value falls insidethe ellipse or ellipsoid (for example, α=0.80). In anotherimplementation, a Projection Statistics PS_(i) distance measure is usedin which the sample mean and covariance are replaced by the samplemedian and the median absolute deviation.

Covariance Propagation

Regarding covariance propagation, a robust form of the covariance matrixof the 3D joint location estimates is maintained by using a weightingscheme that depends on the probabilities determined by MD_(i) or PS_(i).In particular, the robust mean μ_(R) and the robust covariance COV_(R)are determined as:

$\mu_{R} = {\left\lbrack {\sum\limits_{i = 1}^{m}\; w_{i}} \right\rbrack^{- 1} \cdot \left\lbrack {\sum\limits_{i = 1}^{m}\;{w_{i}x_{i}}} \right\rbrack}$${COV}_{R} = {\left\lbrack {{\sum\limits_{i = 1}^{m}\; w_{i}} - 1} \right\rbrack^{- 1} \cdot \left\lbrack {\sum\limits_{i = 1}^{m}\;{\left( {{w_{i}x_{i}} - \mu} \right)\left( {{w_{i}x_{i}} - \mu} \right)^{\prime}}} \right\rbrack}$

In equations above, w_(i) are weights computed from the probabilities bymeans of:w _(i)=min [1,(χ_(n,α) ² /MD _(i) ²)]w _(i)=min [1,(χ_(n,α) ² /PS _(i) ²)]

In the equations above, α represents the probabilities.

FIG. 25 shows one implementation of a probability distribution function(sample covariance matrix) 2500 that illustrates outlier-robustcovariance propagation in accordance with one implementation of thetechnology disclosed. In FIG. 25 , the X-axis represents the covariancedistribution from a prior frame 1 at time t₁. The Y-axis represents 3Djoint estimates (circles) for a single joint from multiple expertnetworks 112 in the current frame 2 at time t₂. The dashed lines in FIG.25 represent the distances of the 3D joint estimates (circles) from theprobability distribution function (sample covariance matrix) 2500. μrepresents the mean of the probability distribution function 2500 in theprior frame 1 at time t₁. FIG. 26 illustrates the probabilities 2600 ofthe distances of the 3D joint estimates (circles) in current frame 2 attime t₂ from the probability distribution function (sample covariancematrix) 2500 calculated in FIG. 25 . Probabilities 4100 serve as weightsthat are applied to each of the 3D joint estimates (circles) in currentframe 2 at time t₂ when an updated sample covariance matrix iscalculated for the next frame. This way, the 3D joint estimates(circles) that are farther from the probability distribution function(sample covariance matrix) 2500 and have lower probabilities 2600 and inturn lower weights contribute less to the updated sample covariancematrix that is propagated to the next frame. In the example shown inFIG. 26 , the 3D joint estimates (circles) have low weights and thuscontribute less to the updated sample covariance matrix shown in FIG. 27. In contrast, the 3D joint estimates (circles) in the center contributemost to the updated sample covariance matrix shown in FIG. 27 .

FIG. 27 shows one implementation of a sample covariance matrix 2700propagated from a prior frame 2 to a current frame 3 at time t₃. In FIG.27 , the black-lined curve represents the updated covariancedistribution from prior frame 2. The grey-lined-dashed curve representsthe previous covariance distribution from prior-prior frame 1 shown inFIG. 25 and FIG. 26 . The difference between the black-lined curve andthe grey-lined-dashed curve illustrates how the sample covariance matrixpropagates and updates from one frame to the next. In addition, the meanof the probability distribution also updates from one frame to the next.This is illustrated by the new updated mean μ′ shown as grey ellipsecompared to the prior mean μ shown in a transparent grey ellipse.

Thus, the outlier-robust covariance propagation prevents erroneous orless accurate estimates from influencing the final hand pose estimates.For instance, if out of thirty (30) expert networks 112, twenty-seven(27) give erroneous estimates that are detected as outliers, then thatwould not negatively influences the estimation of the final hand poseand the three (3) correct and accurate estimates, that were detected asinliers, would dominate the final hand pose estimation.

FIG. 28 shows one implementation of a plurality of 3D joint locationestimates 2800 produced by a plurality of expert networks 112 for asingle hand joint. In the example shown in FIG. 28 , nine (9) expertnetworks 1-9 produced nine (9) 3D joint location estimates for the sameparticular hand joint. In FIG. 29 , a covariance distribution 2900 andmean μ for the 3D joint location estimates 2800 is calculated forcurrent frame 1 at time t₁. In FIG. 30 , new 3D joint location estimates3000 produced by a plurality of expert networks 112 for the same handjoints shown in FIGS. 28 and 29 are received. New 3D joint locationestimates 3000 are captured in current frame 2 at time t₂. In FIG. 30 ,previous 3D joint location estimates 2800 are represented usingdotted-line ellipses and new 3D joint location estimates 3000 arerepresented by light-grey and dark-grey ellipses. Light-grey ellipsesrepresent those new 3D joint location estimates 3000 that are determinedto be inliers based on their distance from the mean μ and the priorcovariance distribution 2900. Dark-grey ellipses represent those new 3Djoint location estimates 3000 that are determined to be outliers basedon their distance from the mean μ and the prior covariance distribution2900. In FIG. 31 , the distances of the inlier and outlier 3D jointlocations of frame 2 are converted into probability-based weights andare used to determine a new covariance distribution 3100 at time t₃. InFIG. 31 , the difference between the previous covariance distribution2900 (dotted-grey-transparent ellipse) and the new covariancedistribution 3000 (bold-black ellipse) is also depicted. Also depictedis the updated mean μ′. In the discussion infra, for clarity's sake, theoutlier-robust covariance propagation was illustrated for only a singlejoint. But, the outlier-robust covariance propagation is simultaneouslyand concurrently calculated for all twenty-eight (28) joints of thehand.

FIGS. 32A, 32B, 32C and 32D show a temporal sequence of theoutlier-robust covariance propagations 3200A, 3200B, 3200C and 3200Dsimultaneously and concurrently calculated for all twenty-eight (28)joints of the hand. In FIGS. 32A, 32B, 32C and 32D, the bigspheres/ellipsoids represent the 28 hand joints and smallerspheres/ellipsoids within each of the 28 hand joints represent jointlocations estimated by the expert networks 112 for the respective 28hand joints. From FIG. 32A up to FIG. 32D, the covariance propagationchanges and in turn updates the joint locations and the pose of the handas new estimates are received from expert networks. As discussed infra,this joint-by-joint estimation detects even the most granular and subtleof hand movements such as fingertip bend and changes in joint angles andjoint locations. Also shown in FIGS. 32A, 32B, 32C and 32D is that theoutlier-robust covariance propagations 3200A, 3200B, 3200C and 3200Dform a valid anatomically-correct hand.

In other implementations, the outlier-robust covariance propagation isperformed using other hand parameters such as joint angles, fingersegment lengths, and others discussed supra.

FIG. 33 shows a representative method 3300 of hand pose estimation usingoutlier-robust covariance propagation in accordance with oneimplementation of the technology disclosed. Flowchart 3300 can beimplemented at least partially with a computer or other data processingsystem, e.g., by one or more processors configured to receive orretrieve information, process the information, store results, andtransmit the results. Other implementations may perform the actions indifferent orders and/or with different, fewer or additional actions thanthose illustrated in FIG. 33 . Multiple actions can be combined in someimplementations. For convenience, this flowchart is described withreference to the system that carries out a method. The system is notnecessarily part of the method.

At action 3302, a first set of estimates of hand position parameters arereceived from multiple generalist and/or specialist neural networks foreach of a plurality of hand joints, as discussed infra.

At action 3304, for each individual hand joint, simultaneouslydetermining a principal distribution of the first set of estimates, asdiscussed infra. In one implementation, a principal distribution isdetermined using a covariance of the first set of estimates.

At action 3306, a second set of estimates of hand position parametersare received from multiple generalist and/or specialist neural networksfor each of the plurality of hand joints, as discussed infra.

At action 3308, for each individual hand joint, simultaneouslycalculating a similarity measure between the second set of estimates andthe principal distribution of the first set of estimates, as discussedinfra. In one implementation, the similarity measure is a distancemeasure such as a Mahalanobis distance and/or Euclidean distance.

At action 3310, for each individual hand joint, simultaneouslyidentifying outliers and inliers in the second set of estimates based onthe similarity measure, as discussed infra.

At action 3312, for each individual hand joint, simultaneouslycalculating contribution weights for the outliers and the inliers basedon the similarity measure, as discussed infra.

At action 3314, for each individual hand joint, simultaneouslydetermining a principal distribution of the second set of estimatesbased on the contribution weights of the outliers and the inliers, asdiscussed infra. In some implementations, final hand position parametersare determined by minimizing an approximation error between the multipleset of estimates.

Hand Model Fitting

In one implementation, a single hand is computed and fitted 116 from thetracked covariance by minimizing approximation error betweencorresponding 3D joint estimates. In some implementations the covarianceupdates are performed in absolute 3D coordinates. When covarianceupdates are completed using absolute 3D coordinates, some covariancecenters may not necessarily form a valid anatomically-correct hand. Thistechnical problem is resolved by applying various smoothing techniquesto such covariance centers, including, but not limited to, additivesmoothing, Kalman filter, kernel smoother, Laplacian smoothing,recursive filter, Savitzky-Golay smoothing filter, local regression,smoothing spline, Ramer-Douglas-Peucker algorithm, exponentialsmoothing, Kolmogorov-Zurbenko filter, or any combination thereof.

Once the final joint locations for each of the twenty-eight (28) handjoints are determined, the depth information for each of the joints iscomputed by calculating the 3D offsets of the respective joints relativeto the center of the so-called “ImageRect.” This is particularly usefulbecause the depth information is determined using a single ImageRectcomputed for a single camera and thus obviates the need of stereoscopicimages or multiple cameras. Furthermore, convolutional neural network101 also determines, during training 100, whether particular joints arebelow or above the ImageRect. In other implementations, the depthinformation for each of the joints is augmented by the use of stereoinformation in the input image data 402 as a multi-channel input. In yetother implementations, the depth information for each of the joints isaugmented by the use of RGB components in the input image data 402 as amulti-channel input.

Once the depth information of each of the twenty-eight (28) joints isdetermined using their respective 3D offsets from the singularImageRect, the 3D joint locations of the twenty-eight (28) hand jointsare converted from image coordinates into world coordinates usinginverse transformation. In one implementation, the D joint locations ofthe twenty-eight (28) hand joints are multiplied by a hand scale (e.g.,based on palm width) to project them into a world coordinate system.

Once the 3D joint locations of the twenty-eight (28) hand joints arerepresented in a world coordinate system, different hand fittingtechniques are applied to generate the final fitted hand. Inimplementation, a rigid alignment of the palm is calculated using theKabsch algorithm. In such an implementation, determining atransformation can include calculating a rotation matrix that provides areduced RMSD (root mean squared deviation) between two paired sets of 3Djoint locations. One implementation can include using Kabsch Algorithmto produce a rotation matrix. The Kabsch algorithm can be used to findan optimal rotation R and translation T that minimizes the error:RMS=sqrt(Σ(R*x _(i) +T−y _(i))^(t)*(R*x _(i) +T−y _(i)))w _(i)

The transformation (both R and T) are applied rigidly to the 3D jointlocations of the twenty-eight (28) hand joints, according to oneimplementation. The 3D joint location matching and rigid alignment isrepeated until convergence. In one implementation, the Kabsch isextended to co-variances by the following minimizing:Σ(R*x _(i) +T−y _(i))^(t) *M _(i)*(R*x _(i) +T−y _(i))

In the equation above, M_(i) is a positive definite symmetric matrix. Inother implementations and by way of example, one or more force lines canbe determined from one or more portions of a virtual surface.

Further, a robust inverse-kinematic (IK) solver is used to determine thefinger angles based on the 3D joint locations of the twenty-eight (28)hand joints. Finally, arm angle parameters are determined using aseparate filtered elbow position. FIG. 34 illustrates one implementationof a fitted hand 3400 based on the 3D joint locations of thetwenty-eight (28) hand joints. In FIG. 34 , the left and rightImageRects are shown in yellow, the 3D joint locations of thetwenty-eight (28) hand joints are shown in different colors, theindividual master and expert pose estimates are shown inside eachcovariance in different colors and the final fitted hand 5200 is shownin pale yellow-green.

Initialization

During testing 200, in one implementation, initialization 206 includesdetecting a new hand entering a field of view of the gesture recognitionsystem and rendering a virtual hand pose based on the 3D position androtation of the hand detected in an image comprising testing data 202.In some implementations, a parallax candidate module is used to generatea parallax map for each of the detected stereoscopic images comprisingtesting data 202. In other implementations, a low or high resolutionsaliency map or disparity map for each of the detected stereoscopicimages comprising testing data 202 is generated. However, a parallax maphas advantage over a saliency map or disparity map because a parallaxmap is computationally inexpensive. The parallax map highlights objectsthat are closer to the cameras of the gesture recognition system andrepresents such objects as bright point clouds. In otherimplementations, gradient images and/or temporal difference images areused to generate the bright point clouds.

In one implementation, one or more hands, along with other objects inthe images, are represented in the parallax maps as bright point clouds.Further, candidate boxes are drawn around each of these bright pointclouds in the parallax maps, which are referred to as “candidate regionsof interest (ROI).” Advancing ahead, for each such candidate ROI in boththe parallax maps, a depth parameter is determined by first convertingthe two-dimensional (2D) candidate ROI into one-dimensional (1D)signals. These 1D signals are generated for each candidate ROI in boththe parallax maps by summing the pixel rows of the respective candidateROI into 1D waveforms that represent the respective 2D candidate ROI.Once the 1D waveform signals are generated from the parallax maps foreach of the 2D candidate ROI, they are respectively convoluted acrossthe alternative stereoscopic image to find the most matchingcounterparts of the 1D waveform signals based on the horizontal offset.In one implementation, a normalized cross-correlation (NCC) and/or aweighted NCC is used to determine, for each 1D waveform signal, the mostmatching counterpart in the alternative stereoscopic image. Further, the1D waveform signals and their respective most matching counterparts areused to perform stereo matching and generate depth estimates for each ofthe candidate ROI.

In addition, for each of the candidate ROI, a spatial normalization isperformed to determine an initial rotation of the candidate ROI. Spatialnormalization includes detecting the pixel gradients of the candidateROI and computing a gradient-direction for those pixel gradients,according to one implementation. The gradient-direction provides thedominant or principal orientation for each of the candidate ROI.Further, a so-called “ImagePatch” is generated based on the dominant orprincipal orientation of the contents of the candidate ROI. FIG. 35Aillustrates one implementation of spatial normalization 3500A. In FIG.35A, the asterisks (*) in white represent the gradient points of thecandidate ROI 3501. In addition, the arrows represent the principalvector (PV) 3506 of rotation calculated based on the gradient-directionand the circle represents the center of mass 3504 of the candidate ROI3501. As shown, the principal vector (PV) 3506 has a rotation differentfrom the candidate ROI 3501. Thus, a 3D ImagePatch 3508 (pitch black) isgenerated with a rotation matching the rotation of PV 3506 and centermatching the center of mass 3504. Further, an in-plane rotation isperformed so that the PV 3506 points upwards after the rotation. Then, amatching in-plane rotation is performed on the ImagePatch 3508. Finally,the rotated ImagePatch 3508 is extracted, as shown in FIG. 35B. FIG. 35Cshows other examples of extracted ImagePatches 3500C. In oneimplementation, ImagePatches are extracted for both, left and right,stereoscopic images, which in turn is used to compute depth information.In some implementations, ImagePatches are assigned a fixed size of 32×32and are grayscale images. In one implementation, ImagePatches areextracted from training data 102 (including both real and simulatedimages) during training 100 as part of pre-processing 103. In anotherimplementation, ImagePatches are extracted from testing data 102(including real images) during testing 200 as part of pre-processing103.

Once the ImagePatches are extracted, they are subjected to a pluralityof initialization heuristics that determine one or more characters ofthe ImagePatches. In one implementation, these heuristics determine howfar the hand is based on the 3D depth information of the ImagePatches.In another implementation, the heuristics check a trajectory of the handto determine whether the hand is a right or a left hand. In yet anotherimplementation, the heuristics determine whether the hand is ananatomically correct hand. In a further implementation, the heuristicsdetermine whether the hand is at arm-length from the camera(s) of thegesture recognition system. In another implementation, the heuristicsdetermine whether the hand overlaps with another hand. In someimplementations, these heuristics are maintained as “IF STATEMENTS.”

Advancing further, the extracted 3D ImagePatches and the results of theheuristics are fed to a so-called “classifier neural network” that istrained on a plurality of real and simulated hand images. The task ofthe classifier neural network is to determine, using the pixel contentsof the 3D ImagePatches and the outcomes of the heuristics, whether theImagePatches represent a hand or not. 3D ImagePatches, which pass theclassifier as hands (determined from threshold scores), are instantiatedusing a 3D virtual hand. This 3D virtual hand has a rotation matchingthe rotation of the ImagePatches and a 3D position based on the 2Dpositions of the corresponding candidate ROI 3501 and their respective3D depth information determined from the 1D signal waveforms, asdiscussed infra. A 3D virtual hand 3500D initialized for the ImagePatch3508 is shown in FIG. 35D.

In some implementations, a pitch angle of the ImagePatch 3508 isdetermined between a negative z-axis of the gesture recognition systemand the projection of a normal vector onto the y-z plane. The pitchrepresents the rotation of the ImagePatch 3508 around the x-axis. In oneimplementation, if the normal vector points upward, the returned angleis between 0 and pi radians (180 degrees). In another implementation, ifthe normal vector points downward, the returned angle is between 0 and−pi radians. In some implementations, a yaw angle of the ImagePatch 3508is determined between a negative z-axis of the gesture recognitionsystem and the projection of a normal vector onto the x-z plane. The yawrepresents the rotation of the ImagePatch 3508 around the y-axis. In oneimplementation, if the normal vector points to the right of the negativez-axis, then the returned angle is between 0 and pi radians (180degrees). In another implementation, if the normal vector points to theleft, then the returned angle is between 0 and −pi radians. In someimplementations, a roll angle of the ImagePatch 3508 is determinedbetween a y-axis of the gesture recognition system and the projection ofa normal vector onto the x-y plane. The roll represents the rotation ofthe ImagePatch 3508 around the z-axis. In one implementation, if thenormal vector points to the left of the y-axis, then the returned angleis between 0 and pi radians (180 degrees). In another implementation, ifthe normal vector points to the right, then the returned angle isbetween 0 and −pi radians. For example, if the normal vector representsthe normal to the palm region of the ImagePatch 3508, then the rollangle provides the tilt or roll of the palm plane compared to thehorizontal (x-z) plane.

Further, bounded hand place referred to as an “ImageRect” is definedbased on the extracted ImagePatch, both during training 100 and testing200. In one implementation, ImageRect has a rectangle center thatmatches the palm center of the ImagePatch 3508. Then, an axis is definedfrom this rectangle center to one or more cameras of the gesturerecognition center. Advancing ahead, one or more normal vectors areprojected on to the planes formed by the rectangle center and normalvectors. Then, a principal direction of the ImagePatch 3508 is used tocompute an angle of rotation for pitch, yaw and roll, as discussedinfra. In some implementations, the normal vectors point perpendicularlyout of the ImagePatch 3508 and the principal direction vector pointsforward. In one implementation, ground truth ImageRects are calculatedfor the ground truth hand in the training data 102. In someimplementations, jitter is added to these ground truth ImageRects in theform of Gaussian noise to the position and rotation angles and thejitter results are added to the training data 102 and fed to theconvolutional neural network 101. During testing 200, the ImageRects areused without the jitter. The jittered ground truth ImageRects duringtraining 100 allow the convolutional neural network 101 to better handlemisaligned ImageRects during testing 200. In particular, during testing200, this allows the convolutional neural network 101 to better trackfast hand movements from one frame to the next. FIG. 36 shows oneimplementation of ImageRects 3600 fitted on an ImagePatch (in yellow).

During training 200, once the hand is initialized, tracking is performedby updating each ImageRect across frames using prior hand movements toextrapolate the ImageRect forward in time. These predictions allowstracking of the very fast and sudden hand movements without the handleaving the ImageRect. When the hand completely exits the field of view,the corresponding ImageRect and ImagePatch are removed from the list oftracked objects to be updated and processed, according to oneimplementation. Furthermore, after initialization 206, the ImageRect isupdated from frame to frame based on the direction and center of thelast estimated hand pose estimates. In some instances, if the ImageRectis not aligned with the direction and center of the tracked hand poseestimate, in the subsequent frame, the ImageRect is updated to havingdirection and center of the last tracked hand pose estimate. As aresult, a fast moving hand that causes misalignment of the ImageRect andthe captured hand images is accounted for by updating, the ImageRect'sposition and center based on the hand poses estimate of the fast movinghand calculated by the convolutional neural network 101 in thesubsequent frame.

Thus, according to one implementation, the previous frame's fitted handmodel (multi-colored ellipses/ellipsoid) is extrapolated 3700 into thecurrent frame's timestamp (shown in FIG. 37 ), followed by extraction ofImageRects and ImagePatches based on the predicted hand model, followedby extraction of features from the ImagePatches by convolution layers104, followed by pose estimation by the fully connected layers ornetworks 118, followed by a combination of individual point estimatesusing outlier-robust covariance propagation, and fitting of a final handmodel to the updated covariance positions.

FIG. 38 shows a representative method 3800 of initialization 206 of ahand in accordance with one implementation of the technology disclosed.Flowchart 3800 can be implemented at least partially with a computer orother data processing system, e.g., by one or more processors configuredto receive or retrieve information, process the information, storeresults, and transmit the results. Other implementations may perform theactions in different order and/or with different, fewer or additionalactions than those illustrated in FIG. 38 . Multiple actions can becombined in some implementations. For convenience, this flowchart isdescribed with reference to the system that carries out a method. Thesystem is not necessarily part of the method.

At action 3802, a new hand is detected in a field of view of a gesturerecognition system, as discussed infra.

At action 3804, one or more candidate regions of interest (ROI) areidentified for an image including the new hand, as discussed infra.

At action 3806, depth information for each of the candidate ROI isdetermined, as discussed infra.

At action 3808, a gradient direction and center of mass is determinedfor each of the candidate ROI, as discussed infra.

At action 3810, for each candidate ROI, an ImagePatch is initializedbased on the gradient direction and the center of mass, as discussedinfra.

At action 3812, the ImagePatch is extracted for each of the ImagePatchand a plurality of hand heuristics are applied on each of the extractedImagePatch, as discussed infra.

At action 3814, for each candidate ROI, the extracted ImagePatch and theresults of the hand heuristics are fed to a hand classifier neuralnetwork that determines whether the extracted ImagePatch resembles ahand, as discussed infra.

At action 3816, a 3D virtual hand is initialized that matches therotation and 3D position of a particular ImagePatch identified as a handby the hand classifier neural network, as discussed infra.

Experimental Results

FIGS. 39A, 39B, 39C, 39D, 39E, 39F, 39G, 39H, 39I, 39J, 39K, 39L, 39M,39N and 39O show multiple frames in a time continuous gesture sequenceof hand poses 3900A, 3900B, 3900C, 3900D, 3900E, 3900F, 3900G, 3900H,3900I, 3900J, 3900K, 3900L, 3900M, 3900N and 3900O represented byskeleton hand models fitted to joint covariances in for the gesturesequences. In FIGS. 39A, 39B, 39C, 39D, 39E, 39F, 39G, 39H, 39I, 39J,39K, 39L, 39M, 39N and 39O, both the joint covariances and thecorresponding fitted skeleton hand are shown for respective estimatedhand poses. As demonstrated by the variety of poses 3900A, 3900B, 3900C,3900D, 3900E, 3900F, 3900G, 3900H, 3900I, 3900J, 3900K, 3900L, 3900M,3900N and 3900O, the technology disclosed tracks in real time the mostsubtle and minute hand gestures, along with most extreme hand gestures.

Augmented Reality (AR)/Virtual Reality (VR) Interactions

FIGS. 40A, 40B and 40C show one implementation of skeleton hand modelsfitted to estimated joint covariances interacting with and manipulating4000A, 4000B and 4000C virtual objects (e.g., depicted boxes) in anaugmented reality (AR)/virtual reality (VR) environment 5600.

Generating Training Data

The major difficulty in hand pose estimation is that the human hand iscapable of an enormous range of poses, which are difficult to simulateor account for. For a neural network to accurately generalize over awide assortment of hand poses, it must be trained over huge volumes ofhand pose variants. Researchers have created libraries of real-worldhand poses, but these libraries are restricted to only a few hundredthousand or few million hand images and the space of hand poses is muchgreater. In addition, the task of accurately labelling thousands andmillions of images with the desired output is impractical. Theimpracticality stems not only from the enormity of the task of labelingmillions of images but also from the fact that, due to occlusion and lowresolution, annotators disagree on what pose label should be assigned toa hand image. As a result, the technical problem of collecting andaccurately labeling enormous amount of hand pose data remains unsolved.

The technology disclosed provides a computer graphic simulator 4100 thatprepares sample simulated hand positions of gesture sequences fortraining of neural networks. Simulator 4100 includes simulationparameters that specify a range of hand positions and gesture sequences.It also specifies a range of hand anatomies, including palm size,fattiness, stubbiness and skin stone. Simulator 4100 also generates andapplies different combinations of backgrounds to the hand positions andgesture sequences. Simulator 4100 also sets simulation parameters forcamera perspective specification, including focal length, horizontal andvertical field of view of the camera, wavelength sensitivity, fielddistortions and artificial light conditions.

The technology disclosed generates between hundred thousand (100,000)and one billion (1,000,000,000) simulated hand positions and gesturesequences with varying hand-anatomy and hand-background simulations.Furthermore, each simulation is labeled with fifteen (15) to forty-five(45) hand position parameters such as 3D joint locations, according toone implementation. In other implementations, different hand positionparameters are used for labeling the ground truth feature vector,including joint angles, capsule hand models, skeleton hand models,volumetric hand models and/or mesh hand models, muscle hand models, eachin 2D and/or 3D space.

Also, the technology disclosed applies the camera perspectivespecification to render from the simulations at least a correspondinghundred thousand (100,000) and one billion (1,000,000,000) simulatedhand images. In one implementation, these simulated hand images are amonocular image. In another implementation, these simulated hand imagesare binocular pairs of images. In one implementation, a simulatedgesture sequence of poses connected by hand motions over a short timespan is generated. A simulated gesture sequence comprises of a pluralityof simulated hand images organized in a sequence of frames. Oncegenerated, the simulated hand images along with the labelled handposition parameters from corresponding simulations are used for trainingconvolutional neural network 101.

Computer Graphics Simulator

First, computer graphics simulator 4100 obviates the problem of manuallabeling of hand images because it automatically generates simulatedhand images along with precise hand position parameters. Second,simulator 4100 nearly covers the entire space of all possible hand posesby generating unbounded number of varying hand poses. In oneimplementation, simulator 4100 receives a specification of a range ofsimulation parameters and uses the specification to automaticallygenerate different combinations of hand images with varying valueswithin the range. FIG. 41 illustrates one implementation of a computergraphics simulator 4100 that includes a simulated coordinate system4101, simulated hand 4102, simulated perspective 4104 of a simulatedgesture recognition system (GRS) 4105, simulated hand images 4106,gesture sequence player 4108, gesture sequence objects 4110, device,image, hand and scene attributes 4112 and rendering attributes 4114. Inother implementations, simulator 4100 may not have the same elements asthose listed above and/or may have other/different elements instead of,or in addition to, those listed above. The different elements can becombined into single software modules and multiple software modules canrun on the same hardware.

Ground Truth Pose Vector

FIG. 54 shows one implementation of the simulated hand images (left andright, (l, r)) 4106 generated by simulator 4100 and the correspondinglabel assigned or mapped 5400 to the images 4106 in the form of theground truth 84 (28×3) dimensional pose vector 5412 of 3D jointlocations of twenty-eight (28) hand joints. Because the simulator 4100knows the hand position parameters of the simulated hand 4102 in thesimulated coordinate system 4101, the pose vector 5412 is computed bythe simulator 4100 as the ground truth label corresponding to thesimulated hand images 4106. Simulated hand 4102 has twenty-seven (27)degrees of freedom, four (4) in each finger, three (3) for extension andflexion and one (1) for abduction and adduction, according to oneimplementation. The thumb of the simulated hand 4102 has five (5)degrees of freedom, with six (6) degrees of freedom for the rotation andtranslation of the wrist, according to one implementation. Thus,simulated hand 4102 closely mimics the poses and motions of a real hand.Regarding simulated coordinate system 4101, in one implementation, it isa right-handed Cartesian coordinate system, with the origin centered atthe top of the simulated gesture recognition system 4105. In oneimplementation, the x- and z-axes of the simulated coordinate system4101 lie in the horizontal plane, with the x-axis running parallel tothe long edge of the simulated gesture recognition system 4105. In oneimplementation, the y-axis is vertical, with positive values increasingupwards or downwards. In one implementation, the z-axis has positivevalues increasing towards the simulated hand 4102. The images 4106 andthe corresponding pose vector 5412 are stored by simulator 4100 inmemory as pairs 5400 during training 100. So, when convolutional neuralnetwork 101 receives as input images similar to or like images 4106, itinvokes the memory for the corresponding pose vector 5412 and producesit as output. In other implementations, pose vector 5412 is comprised ofjoint angles, capsule hand model parameters, skeleton hand modelparameters, volumetric hand model parameters and/or mesh hand modelparameters, muscle hand model parameters, each in 2D and/or 3D space.

In one implementation, simulator 4100 defines pose vector 5412 in termsof angles of skeleton model such as yaw, pitch, roll, bend, tilt, andothers. In such an implementation, a yaw, pitch, roll, bend or title foreach of the twenty-eight (28) joints of the simulated hand 4102 aredefined, for example, four (4) parameters for each of fingers and three(3) parameters for the thumb of the simulated hand 4102, along withrotation and translation of the palm of the simulated hand 4102.Further, other parameters of the simulated hand 4102, discussed supra,such as scale, fattiness, skin tone, stubbiness (which controls theratio of the fingers to palm) are defined. Once the simulationparameters are defined, they are used by a rendering engine to generatethe simulated hand 4102. In one implementation, a rendering type of thesimulated hand 4102 is defined by the rendering attributes 4114.Rendering attributes 4114 are configured to generate a realistic 3D meshmodel or a rigged mesh hand, according to one implementation of thesimulated hand 4102 shown in FIG. 41 . In another implementation of thesimulated hand 4102 shown in FIG. 50 , rendering attributes 4114 areconfigured to generate a 3D capsule model. FIG. 50 shows oneimplementation of generating simulated hand poses and gesture sequencesas 3D capsule hand models 5000 using a computer graphic simulator 4100.In other implementations, different hand models, such as volumetricmodels, muscle models, skeleton models are used to generate thesimulated hand 4102. In one implementation, the ground truth pose vector5412 is divided by the palm width of the simulated hand 4102 in order tomake the units scale-invariant and stored in memory. This is usefulbecause, during testing pipeline 200, the depth of a hand is determinedbased on its scale since a large object viewed from further away looksmostly the same as a small object closer to the camera of the gesturerecognition system.

In addition to be being used for generating the simulated hand 4102, thedefined simulation parameters are also used to compute the ground truthhand position parameters of the pose vector 5412. These hand positionparameters include simulation parameters like joint locations and jointangles, and others, as discussed supra. In one implementation, the posevector 5412 is generated by computing, for capsule solids representingeach individual hand bones (e.g., fingers, thumb, palm, wrist, elbow),joint angles and joint locations. Once computed, the ground truth handposition parameters of the pose vector 5412 such as joint angles andjoint locations are stored in memory to label the simulated input handimages 4106 with the pose vector 5412.

Simulated Hand Positions and Gesture Sequences

Simulator 4100 generates simulation hand images 4106 from theperspective or viewpoint of the simulated gesture recognition system4105 that represents a real gesture recognition system used by thetechnology disclosed and trained as part of convolutional neural network101. In the example shown in FIG. 41 , such as real gesture recognitionsystem is a Leap Motion Controller™, which is a motion sensing deviceintroduced by Leap Motion, Inc., San Francisco, Calif. In oneimplementation, the real gesture recognition system is a dual-cameramotion controller that is positioned and oriented to monitor a regionwhere hand motions normally take place. In some implementations, thegesture recognition system uses one or more LED emitters to illuminatethe surrounding space with IR light, which is reflected back from thenearby objects and captured by two IR cameras. In anotherimplementation, the real gesture recognition system is a 3Dtime-of-flight camera that illuminates the scene with a modulated lightsource to observe the reflected light. In yet another implementation,the real gesture recognition system is a structured-light 3D scannerthat uses infrared structured-light pattern to determine geometricreconstruction of the object shape. In some implementations, the realgesture recognition system captures between hundred (100) and threehundred (300) frames per second. Thus, during training pipeline 100,simulator 4100 generates simulated training data 102 from a perspectiveor viewpoint that almost exactly matches the perspective or viewpoint ofthe actual gesture recognition system from which the testing data 202 iscaptured and fed into the convolutional neural network 101 duringtesting pipeline 200. As a result, convolutional neural network 101generates hand pose estimates that accurately represent a hand gesturein an image because discrepancy or the inconsistency between thetraining data 102 and the testing data 202 is minimized with regards tothe perspective or viewpoint of the gesture recognition system.

FIG. 46 shows one implementation of generating a simulated gesturesequence 4600 of simulated mesh hands 4102. In FIG. 46 , simulationparameters 4110, 4112 and 4114 of a simulated mesh hand 4102 are editedor modified by selecting the simulated hand 4102. The selection ismarked by a visual coding (e.g., green) of the selected hand (right handshown in FIG. 46 ). In other implementations, different visual codingssuch as patterns or notifications, etc. are used. Once a hand isselected, various simulation parameters 4110, 4112 and 4114 of theselected hand such as position, shape, size, etc. are adjusted by movingor re-shaping the hand or its sub-components like fingers, thumb, palm,elbow in the simulated coordinate system 4101. Thus, in thisimplementation, the simulation parameters 4110, 4112 and 4114 are notset or modified using input field values, but instead by moving the handor hands in the simulated coordinate system 4101 using a point andselection command generated by an input device. This non-input-fielddefinition is referred to as “natural traversing” of the simulated hands4102 and is used to generate various trajectories of different simulatedgesture sequences 4600, 4700, 4800, 5000 and 5100 that mimic realisticgesture movements of a real hand. As shown in FIG. 46 , FIG. 47 and FIG.48 , moving the simulated hands 4102 in the simulated coordinate system4101 automatically updates the simulation parameters 4110, 4112 and 4114of the hands without requiring explicit field input. In addition,natural traversing not only updates the location parameters of the handsbut also updates other parameters like biometrics-related simulationparameters, stubbiness-related simulation parameters,joint-location-relation simulation parameters, joint-angle-relatedsimulation parameters, orientation-relation simulation parameters,palm-orientation-related simulation parameters, palm-width-relatedsimulation parameters, finger-bend/yaw/roll/tilt/roll/path-relatedsimulation parameters, finger-length-related simulation parameters(elongation), and others, as discussed supra. FIGS. 50 and 51 representthe simulated hand 4102 using 3D capsule hand models as opposed to meshrigged hand models discussed infra. From FIG. 50 to FIG. 51 , the anglesof hand sub-components like fingers, palm, wrist and elbow of theselected hand (selection indicated by green visual coding) are changedby moving one or more of these sub-components in the simulatedcoordinate system 4101 from a first key frame 5000 to a second key frame5100. In one implementation, an update to a particular simulationparameter or sub-component automatically updates other simulationparameters or sub-components to correspond to realistic hand gesturesand correct hand anatomies. For example, bending of multiple fingersalso automatically cascades into bending of the palm and the elbow ofthe simulated hands 4102.

Gesture sequences are defined using key frames, according to oneimplementation. In one implementation, a series of key frames defineflag point hand position parameters of the simulated hands 4102 and thegesture sequences are then generated by running the simulated hands 4102across each of the defined flag points. For instance, in FIG. 46 , astart key frame is set when the right hand is at a rest position. InFIG. 47 , an intermediate key frame is set when the right hand is stillat an elevated position. In FIG. 48 , a terminal key frame is set whenthe right hand is still at a leftward-elevated position. Once the keyframes and the corresponding hand position parameters for each of thekey frames (e.g., right or left hand, position of the hand) are set,then the gesture sequence is instantiated and automatically renderedacross the key frames, for instance, the right hand starts at a restposition, then elevates and then moves to the left. In otherimplementations, multiple simulation parameters are defined per keyframe and a plurality of key frames (five, ten, fifty, or hundred) aredefined for each gesture sequence. For instance, for the same gesturesequence, a first key frame defines the joint location of the fingers,the second key frame defines the bend of the palm, the third key framedefines the joint angles of the fingers and the thumb and the fourth keyframe defines the bend of the elbow. In other implementations, differentvariations of the simulation parameters discussed supra, and differentvalues and ranges of the simulation parameters are defined across anynumber of key frames to specify one or more gesture sequences. Anexample of modification of a simulation parameter in a given key frame5100 is shown in FIG. 51 . Once a gesture sequence is defined, it isstored in memory and re-rendered upon invocation.

In some implementations, the gesture sequences are also captured usingthe simulated hand images 4106 that mimic real world images fed to theconvolutional neural network 101. Simulated hand images 4106 representthe real world images captured by the real world gesture recognitionsystems digitally represented by the simulated gesture recognitionsystem (GRS) 4105. This representation is based on various device andimage parameters, such as simulation attributes 4112 (e.g., device fieldof view, perspective, depth, image size, image type, image count) andothers discussed supra. For example, in FIG. 46 , FIG. 47 and FIG. 48 ,the simulated hand image 4106 is a grayscale monocular image based on amesh model. In FIG. 49 , the simulated hand images 4106 are grayscalestereoscopic or binocular images 4900 based on a mesh model. In FIG. 52, the simulated hand images 4106 are grayscale stereoscopic or binocularimages 5200 based on a capsule model. This variation across thesimulated hand images 4106, which are used as the input hand images,allow the convolutional neural network 101 to train across an assortmentof inputs and thus generalize better over unseen inputs (not present inthe training data 102). Furthermore, the simulated hand images 4106 areupdated simultaneously as each of the simulation parameters are updatedfrom one key frame to the next. Thus, the simulated hand images 4106 aresensitive even to the minutest updates to the simulation parameters suchas a bend of an index finger of the left hand and are updatedaccordingly to match the simulated hands 4102. This is illustratedbetween FIG. 46 , FIG. 47 , and FIG. 48 , where updates to thesimulation parameters generated corresponding different simulated handimages 4106.

Simulation Parameters

A sample set of configurable simulation parameters used by simulator4100 to generate simulated hand positions and gesture sequences includesthe following:

Gesture Sequence Objects Name Type Left Hand Hand Thumb Finger IndexFinger Middle Finger Ring Finger Pinky Finger Right Hand Hand ThumbFinger Index Finger Middle Finger Ring Finger Pinky Finger Device Device

Device, Image, Hand and Scene Attributes Name Device Position X, Y, ZCoordinates Rotation X, Y, Z Coordinates Horizontal Field of View (HFOV)Value Vertical Field of View (VFOV) Value Baseline (distance betweencameras) Value D. Noise (field distortion (e.g., Gaussian Value Noise,Poisson)) S. Noise (field distortion (e.g., Gaussian Value Noise,Poisson)) Gamma (field distortion) Value Background Color Value LightingStrength (artificial light conditions) Value Left Background Value RightBackground Value Image Type (e.g., greyscale, color, depth) Value ImageSize (e.g., pixels count) Value Image Count (e.g., stereo, mono) ValueImage Model (e.g., mesh, capsule) Value Name Right Hand Position X, Y, ZCoordinates Rotation X, Y, Z Coordinates Occlusion Value Pitch Value YawValue Roll Value Path Value Traj ectory Value Angular Velocity ValueVelocity Value Euler Angles Value Orientation Value Torque Value StressValue Strain Value Shear Value Finger Positions Value Fingers Value PalmPosition Value Palm Orientation Value Palm Velocity Value Palm NormalValue Palm Width Value Direction Value Grab Strength Value PinchStrength Value Finger Segment Length Value Joint Locations Value JointAngles Value Finger Segment Orientation Value Wrist Positions ValueWrist Orientation Value Arm Value Confidence Value Curling Value TorsionValue Acceleration Value Stubbiness Value Gender Value Skin Tone ValueTranslation Value Distance (e.g., mmil) Value Time (e.g., msec) ValueSpeed (e.g., mmil/sec) Value Angle (e.g., radians) Value Name Left HandPosition X, Y, Z Coordinates Rotation X, Y, Z Coordinates OcclusionValue Pitch Value Yaw Value Roll Value Path Value Traj ectory ValueAngular Velocity Value Velocity Value Euler Angles Value OrientationValue Torque Value Stress Value Strain Value Shear Value FingerPositions Value Fingers Value Palm Position Value Palm Orientation ValuePalm Velocity Value Palm Normal Value Palm Width Value Direction ValueGrab Strength Value Pinch Strength Value Finger Segment Length ValueJoint Locations Value Joint Angles Value Finger Segment OrientationValue Wrist Positions Value Wrist Orientation Value Arm Value ConfidenceValue Curling Value Torsion Value Acceleration Value Stubbiness ValueGender Value Skin Tone Value Translation Value Distance (e.g., mmil)Value Time (e.g., msec) Value Speed (e.g., mmil/sec) Value Angle (e.g.,radians) Value

Rendering Attributes Data Transfer Transfer Depths and Normals X, Y, ZCoordinates Transfer Labels X, Y, Z Coordinates Transfer Masks ValuePlayback Time Between Frames (e.g., msec) Value (e.g., 20) Frames perSecond Value (e.g., 50) Number of Frames Value (e.g., 500000)Interpolation Value (e.g., Cubic) Wraparound Value (e.g., Clamp)Multiple Device Timing Value (e.g., Synchronized) Playback Speed Value(e.g., Normal) Rendering Render Mode Type (e.g., FBX, Capsule)

The simulation parameters are configured using interface input fields,in one implementation. In other implementations, the simulationparameters are configured using different interface input methods suchas scroll bars, scroll down menus, lists, voice commands, opticalcommands, buttons, widgets, tabs, and the like. FIG. 42 illustrates agraphical user interface (GUI) implementation of computer graphicssimulator 4100 visually rendering gesture sequence objects 4110 forconfiguration and specification. FIG. 43 illustrates a graphical userinterface (GUI) implementation of computer graphics simulator 4100visually rendering device, image, hand and scene attributes 4112 forconfiguration and specification. FIG. 44 illustrates a graphical userinterface (GUI) implementation of computer graphics simulator 4100visually displaying rendering attributes 4114 for configuration andspecification. FIG. 45 illustrates a graphical user interface (GUI)implementation of computer graphics simulator 4100 visually renderinghand attributes 4112 for configuration and specification.

Automated Range-Based Simulation

Simulator 4100 automatically generates simulations of one-handed ortwo-handed poses by using ranges that serve as specified constraints ofanatomically correct “realistic” hand poses. In one implementation,simulator 4100 instantiates simulation parameters discussed infra acrossa range of values to automatically generate hundred thousand (100,000)to one billion (1,000,000,000) simulated unique hand positions andgestures sequences with varying hand poses, hand anatomies, backgroundsand camera perspectives. Further, simulator 4100 automatically labels ormaps each of the simulated unique hand positions and gestures sequencesto corresponding ground truth hand position parameters like pose vector5412. These ranges are defined between maximum and minimum values ofparticular simulation parameters, such as anatomically correct jointlocations and joint angles of hand components (e.g., distal phalanges,intermediate phalanges, proximal phalanges and metacarpals for each ofthe fingers and thumb, wrist and arm movements), anatomical poses basedon hand components (e.g., distal phalanges, intermediate phalanges,proximal phalanges and metacarpals for each of the fingers and thumb,wrist and arm movements). In one implementation, such maximum andminimum values are expressed in pitch, yaw, scale, translation,rotation, bend, elongation, and the like.

In one implementation of biometrics-related simulation parameters likehand stubbiness, fattiness and skin tone, simulator 4100 automaticallygenerates unique hand positions and gestures sequences with variety ofvalues of such biometrics-related simulation parameters defined within aspecified range. In another implementation of background-relatedsimulation parameters like field distortion using Gaussian noise orPoisson noise, simulator 4100 automatically generates unique handpositions and gesture sequences with a variety of values of suchbackground-related simulation parameters defined within a specifiedrange.

FIGS. 53A, 53B, 53C, 53D, 53E, 53F, 53G, 53H, 53I, 53J and 53K aredifferent examples of automated range-based simulations of differenthand poses generated by simulator 4100. Also, each of the examples has adifferent background that is automatically and randomly applied to itbased on defined background-range simulation parameter. For example,FIG. 53A is a curled-finger pose 5300A with background 1, FIG. 53B is asemi-curled-finger pose 5300B with background 2, FIG. 53C is aone-finger pose 5300C with background 3, FIG. 53D is an open-hand pose5300D with background 4, FIG. 53E is an open-hand plus curled-thumb pose5300E with background 5, FIG. 53F is a loose-fist pose 5300F withbackground 6, FIG. 53G is a loose-fist plus curled-index-finger andcurled-thumb pose 5300G with background 7, FIG. 53H is ahollow-loose-fist pose 5300H with background 8, FIG. 53I is aright-titled-open-hand pose 5300I with background 9, and FIG. 53J is aleft-titled-open-hand plus curled-middle-finger pose 5300J withbackground 10. FIG. 53K is a finger-point plus thumb-out pose 5300K withbackground 11 in the form a 3D mesh model instead of the 3D capsulemodels of FIGS. 53A-53J. In other implementations, each of these exampleposes have different values for the different simulation parameters(like biometrics-related simulation parameters,artificial-light-conditions-related simulation parameters), as discussedinfra.

Regarding gesture sequences, in one implementation, simulator 4100automatically generates gesture sequences by combining variousrange-based simulated poses. For example, each of the individualsimulated poses 5300A, 5300B, 5300C, 5300D, 5300E, 5300F, 5300G, 5300H,5300I, 5300J and 5300K are combined to form a single gesture sequenceacross multiple image frames. Simulated gesture sequences are configuredusing rendering attributes 4114 and assigned simulation parameters liketime between frames of the gesture sequence, number of frames per secondin the gesture sequence, number of frames in the gesture sequence, andothers, according to one implementation. In another implementation,simulated gesture sequences are replayed forward or backward and brokendown temporally by individual hand poses or individual frames using agesture sequence player 4108. Using the gesture sequence player 4108,individual hand poses or individual frames of a gesture sequence areexamined and investigated at a given timestamp. In some implementations,such examination and investigation includes editing the differentsimulation parameters discussed infra at a given hand pose, frame ortimestamp to generate and store a new simulated gesture sequence,variant simulated gesture sequence, morphed simulated gesture sequenceor altered or modified simulated gesture sequence. In oneimplementation, such editing it done using the GUI representations ofthe simulated coordinate system 4101, simulated hand 4102, simulatedperspective 4104 of a simulated gesture recognition system 4105, gesturesequence objects 4110, device, image, hand and scene attributes 4112 andrendering attributes 4114.

Simulated Dedicated Gesture Sequences

In one implementation, simulator 4100 mimics commonly performed handposes and gestures and generates corresponding simulated “dedicated”hand positions and gesture sequences. Some examples of such commonlyperformed hand poses and gestures include a fist, grabbing, open-hand,pinching, finger point, one finger click, two finger point, two fingerclick, prone one finger point, prone one finger click, prone two fingerpoint, prone two finger click, medial one finger point, medial twofinger point, a point and grasp, a grip-and-extend-again motion of twofingers of a hand, grip-and-extend-again motion of a finger of a hand,holding a first finger down and extending a second finger, a flick of awhole hand, flick of one of individual fingers or thumb of a hand, flickof a set of bunched fingers or bunched fingers and thumb of a hand,horizontal sweep, vertical sweep, diagonal sweep, a flat hand with thumbparallel to fingers, closed, half-open, pinched, curled, fisted, mimegun, okay sign, thumbs-up, ILY sign, one-finger point, two-finger point,thumb point, pinkie point, flat-hand hovering (supine/prone),bunged-fingers hovering, or swirling or circular sweep of one or morefingers and/or thumb and/arm.

Each of the simulated dedicated hand positions and gesture sequences isthen subjected to variations of other simulation parameters discussinfra, including biometrics-related simulation parameters,background-related simulation parameters,artificial-light-conditions-related simulation parameters, and others.This generates many more permutations and combinations of each of thesimulated dedicated hand positions and gesture sequences. For example,for every simulated dedicated hand position and gesture sequence, onehundred and twenty (120) variations are generated and stored. Inaddition, different simulated dedicated hand positions are combined indifferent orders to generate different gesture sequences so as toincreasingly cover the space of all possible poses and gestures. Forinstance, a first simulated gesture sequence starts with an open-hand,followed by a pinch, which is followed by a release. Another simulatedsequence starts with an open-hand, followed by a grasp, which isfollowed by a release. All these hand positions and gesture sequencesare generated for both hands, right and left. Furthermore, simulator4100 adds another layer of variation to the training data 102 bygenerating the resulting output in the forms of joint location models,joint angle models, capsule hand models, skeleton hand models,volumetric hand models and/or mesh hand models, muscle hand models, eachin 2D and/or 3D space. A sample list of dedicated hand poses in Pythonprogramming language is presented below:

-   -   “clustered”,    -   “fist”,    -   “finger-movement-0”,    -   “finger-movement-1”,    -   “finger-movement-2”,    -   “grabbing”,    -   “hmdFieldPoses1_R”,    -   “hmdFieldPoses2_R”,    -   “hmdFieldPoses3_R”,    -   “hmdFieldPoses4_R”,    -   “hmdFieldPoses5_R”,    -   “open-hand”,    -   “pinching”,    -   “pointing-new”,    -   “poses3_extended”,    -   “posesMixed_extended”,    -   “sim-long”,    -   “super-long”,    -   “highangle-0”,    -   “highangle-1”,    -   “highangle-2”,    -   “twohand-0”,

The variety of simulation parameters discussed infra and the combinationof various simulated hand positions and gesture sequences makeconvolutional neural network 101 very robust against different types ofhands and hand poses in different backgrounds and clutters. Thus,training convolutional neural network 101 on such a huge and variedtraining data 102 allow it to generalize better on instances of handposes and gestures that it has not seen before. As well, being trainedon realistic and common gesture sequences allows convolutional neuralnetwork 101 to benefit from the knowledge of most likely next orsucceeding pose. Convolutional neural network 101 uses this knowledge inits prediction of the actual next or succeeding pose such that when theprediction differs from the knowledge beyond a set threshold,convolutional neural network 101 automatically corrects the predictionto output a pose estimate that is consistent with the learned gesturesequences of realistic gestures. In other implementations, convolutionalneural network 101 ignores this knowledge and continues to output a poseestimate based on its actual prediction.

Training data 102 also allows convolutional neural network 101 to trainand test data that is generalized to different image types. In oneimplementation, training 100 is performed on grayscale infraredbrightness images. In another implementation, training 100 is performedon color images. In yet another implementation, training 100 isperformed on depth maps to eliminate the need for stereo imageprocessing and background segmentation. To generalize the training data102, simulator 4100 generates simulated grayscale infrared brightnessimages, color images and depth maps or images.

Also, in addition to the simulated data discussed infra, training data102 also includes millions of real world images and frames of hands andgestures collected from the field by Leap Motion, Inc., San Francisco,Calif. Leap Motion, Inc.'s Leap Motion Controller is used by millions ofusers, including a robust developer community of thousands ofdevelopers. Developers use application programming interfaces (APIs)provided by Leap Motion, Inc. to create gesture recognitionapplications. This ecosystem puts Leap Motion, Inc. in a unique positionof accumulating millions of hand images and hand gestures from the realworld, which, along with their rotated, translated and scaled variants,ultimately contribute to and enrich training data 102. This in turnallows convolutional neural network 101 to generalize and train over alarger space of realistic hand poses and gestures.

In some implementations, to solve the problem of “overfitting,” i.e. toprevent certain areas in the pose space from being too denselypopulated, a conservative sparsification pass is applied to the trainingdata 102 based on pose similarity. In one implementation, such asparsification pass eliminates between ten (10) to (20) percent of thetraining data 102. This allows the convolutional neural network 101 togeneralize better over the entire space of possible poses, as opposed tofocusing too heavily on particular over-represented hand poses andgestures.

FIG. 55 shows a representative method 5500 of generating training data102 in accordance with one implementation of the technology disclosed.Flowchart 5500 can be implemented at least partially with a computer orother data processing system, e.g., by one or more processors configuredto receive or retrieve information, process the information, storeresults, and transmit the results. Other implementations may perform theactions in different orders and/or with different, fewer or additionalactions than those illustrated in FIG. 55 . Multiple actions can becombined in some implementations. For convenience, this flowchart isdescribed with reference to the system that carries out a method. Thesystem is not necessarily part of the method.

At action 5502, ground-truth simulated stereoscopic hand images (l, r)for gesture sequences are generated using a computer graphic simulator,as discussed infra.

At action 5504, stereoscopic hand boundaries, referred to as“ImageRects,” are extracted and aligned with hand centers, as discussedinfra.

At action 5506, translated, rotated and scaled variants of thestereoscopic hand boundaries (ImageRects) are generated, as discussedinfra.

At action 5508, Gaussian jittering is applied to the variants of thestereoscopic hand boundaries (ImageRects) to generate additionaljittered ImageRects, as discussed infra.

At action 5510, hand regions, referred to as “ImagePatches,” are croppedfrom the jittered variants of the ImageRects, as discussed infra.

At action 5512, an 84 (28×3) dimensional pose vector of 3D jointlocations of twenty-eight (28) hand joints is computed using thecomputer graphic simulator, as discussed infra.

At action 5514, the 84 dimensional pose vector is stored as the outputlabel for the simulated stereoscopic hand images (l, r), as discussedinfra.

Gesture Recognition

Referring to FIG. 56 , which illustrates an augmented reality(AR)/virtual reality (VR) environment 5600 with a gesture recognitionsystem 5606 for capturing image data according to one implementation ofthe technology disclosed. System 5600 is preferably coupled to awearable device 5601 that can be a personal head mounted device (HMD)having a goggle form factor such as shown in FIG. 56 , a helmet formfactor, or can be incorporated into or coupled with a watch, smartphone,or other type of portable device.

In various implementations, the system and method for capturing 3Dmotion of an object as described herein can be integrated with otherapplications, such as a HMD or a mobile device. Referring again to FIG.56 , a HMD 5601 can include an optical assembly that displays asurrounding environment or a virtual environment to the user;incorporation of the gesture recognition system 5606 in the HMD 5601allows the user to interactively control the displayed environment. Forexample, a virtual environment can include virtual objects that can bemanipulated by the user's hand gestures, which are tracked by thegesture recognition system 5606. In one implementation, the gesturerecognition system 5606 integrated with the HMD 5601 detects a positionand shape of user's hand and projects it on the display of the gesturerecognition system 5606 such that the user can see her gestures andinteractively control the objects in the virtual environment. This canbe applied in, for example, gaming or internet browsing.

Environment 5600 includes any number of cameras 5602, 5604 coupled to agesture recognition system 5606. Cameras 5602, 5604 can be any type ofcamera, including cameras sensitive across the visible spectrum or withenhanced sensitivity to a confined wavelength band (e.g., the infrared(IR) or ultraviolet bands); more generally, the term “camera” hereinrefers to any device (or combination of devices) capable of capturing animage of an object and representing that image in the form of digitaldata. For example, line sensors or line cameras rather than conventionaldevices that capture a two-dimensional (2D) image can be employed. Theterm “light” is used generally to connote any electromagnetic radiation,which may or may not be within the visible spectrum, and may bebroadband (e.g., white light) or narrowband (e.g., a single wavelengthor narrow band of wavelengths).

Cameras 5602, 5604 are preferably capable of capturing video images(i.e., successive image frames at a constant rate of at least 15 framesper second), although no particular frame rate is required. Thecapabilities of cameras 5602, 5604 are not critical to the technologydisclosed, and the cameras can vary as to frame rate, image resolution(e.g., pixels per image), color or intensity resolution (e.g., number ofbits of intensity data per pixel), focal length of lenses, depth offield, etc. In general, for a particular application, any camerascapable of focusing on objects within a spatial volume of interest canbe used. For instance, to capture motion of the hand of an otherwisestationary person, the volume of interest might be defined as a cubeapproximately one meter on each side.

As shown, cameras 5602, 5604 can be oriented toward portions of a regionof interest 5612 by motion of the device 5601, in order to view avirtually rendered or virtually augmented view of the region of interest5612 that can include a variety of virtual objects 5616 as well ascontain an object of interest 5614 (in this example, one or more hands)that moves within the region of interest 5612. One or more sensors 5608,5610 capture motions of the device 5601. In some implementations, one ormore light sources 5615, 5617 are arranged to illuminate the region ofinterest 5612. In some implementations, one or more of the cameras 5602,5604 are disposed opposite the motion to be detected, e.g., where thehand 5614 is expected to move. This is an optimal location because theamount of information recorded about the hand is proportional to thenumber of pixels it occupies in the camera images, and the hand willoccupy more pixels when the camera's angle with respect to the hand's“pointing direction” is as close to perpendicular as possible. Gesturerecognition system 5606, which can be, e.g., a computer system, cancontrol the operation of cameras 5602, 5604 to capture images of theregion of interest 5612 and sensors 5608, 5610 to capture motions of thedevice 5601. Information from sensors 5608, 5610 can be applied tomodels of images taken by cameras 5602, 5604 to cancel out the effectsof motions of the device 5601, providing greater accuracy to the virtualexperience rendered by device 5601. Based on the captured images andmotions of the device 5601, gesture recognition system 5606 determinesthe position and/or motion of object 5614.

For example, as an action in determining the motion of object 5614,gesture recognition system 5606 can determine which pixels of variousimages captured by cameras 5602, 5604 contain portions of object 5614.In some implementations, any pixel in an image can be classified as an“object” pixel or a “background” pixel depending on whether that pixelcontains a portion of object 5614 or not. Object pixels can thus bereadily distinguished from background pixels based on brightness.Further, edges of the object can also be readily detected based ondifferences in brightness between adjacent pixels, allowing the positionof the object within each image to be determined. In someimplementations, the silhouettes of an object are extracted from one ormore images of the object that reveal information about the object asseen from different vantage points. While silhouettes can be obtainedusing a number of different techniques, in some implementations, thesilhouettes are obtained by using cameras to capture images of theobject and analyzing the images to detect object edges. Correlatingobject positions between images from cameras 5602, 5604 and cancellingout captured motions of the device 5601 from sensors 5608, 5610 allowsgesture recognition system 5606 to determine the location in 3D space ofobject 5614, and analyzing sequences of images allows gesturerecognition system 5606 to reconstruct 3D motion of object 5614 usingconventional motion algorithms or other techniques. See, e.g., U.S.patent application Ser. No. 13/414,485, filed on Mar. 7, 2012 and Ser.No. 13/742,953, filed on Jan. 16, 2013, and U.S. Provisional PatentApplication No. 61/724,091, filed on Nov. 8, 2012, which are herebyincorporated herein by reference in their entirety.

Presentation interface 5620 employs projection techniques in conjunctionwith sensory based tracking in order to present virtual (or virtualizedreal) objects (visual, audio, haptic, and so forth) created byapplications loadable to, or in cooperative implementation with, thedevice 5601 to provide a user of the device with a personal virtualexperience. Projection can include an image or other visualrepresentation of an object.

One implementation uses motion sensors and/or other types of sensorscoupled to a motion-capture system to monitor motions within a realenvironment. A virtual object integrated into an augmented rendering ofa real environment can be projected to a user of a portable device 5601.Motion information of a user body portion can be determined based atleast in part upon sensory information received from imaging devices(e.g., cameras 5602, 5604) or acoustic or other sensory devices. Controlinformation is communicated to a system based in part on a combinationof the motion of the portable device 5601 and the detected motion of theuser determined from the sensory information received from imagingdevices (e.g., cameras 5602, 5604) or acoustic or other sensory devices.The virtual device experience can be augmented in some implementationsby the addition of haptic, audio and/or other sensory informationprojectors. For example, an optional video projector 5620 can project animage of a page (e.g., a virtual device) from a virtual book objectsuperimposed upon a real world object, e.g., a desk 5616 being displayedto a user via live video feed; thereby creating a virtual deviceexperience of reading an actual book, or an electronic book on aphysical e-reader, even though no book nor e-reader is present. Optionalhaptic projector can project the feeling of the texture of the “virtualpaper” of the book to the reader's finger. Optional audio projector canproject the sound of a page turning in response to detecting the readermaking a swipe to turn the page. Because it is a virtual reality world,the back side of hand 5614 is projected to the user, so that the scenelooks to the user as if the user is looking at their own hand(s).

A plurality of sensors 5608, 5610 are coupled to the gesture recognitionsystem 5606 to capture motions of the device 5601. Sensors 5608, 5610can be any type of sensor useful for obtaining signals from variousparameters of motion (acceleration, velocity, angular acceleration,angular velocity, position/locations); more generally, the term “motiondetector” herein refers to any device (or combination of devices)capable of converting mechanical motion into an electrical signal. Suchdevices can include, alone or in various combinations, accelerometers,gyroscopes, and magnetometers, and are designed to sense motions throughchanges in orientation, magnetism or gravity. Many types of motionsensors exist and implementation alternatives vary widely.

The illustrated environment 5600 can include any of various othersensors not shown in FIG. 56 for clarity, alone or in variouscombinations, to enhance the virtual experience provided to the user ofdevice 5601. For example, in low-light situations where free-formgestures cannot be recognized optically with a sufficient degree ofreliability, gesture recognition system 5606 may switch to a touch modein which touch gestures are recognized based on acoustic or vibrationalsensors. Alternatively, gesture recognition system 5606 may switch tothe touch mode, or supplement image capture and processing with touchsensing, when signals from acoustic or vibrational sensors are sensed.In still another operational mode, a tap or touch gesture may act as a“wake up” signal to bring the gesture recognition system 5606 from astandby mode to an operational mode. For example, the gesturerecognition system 5606 may enter the standby mode if optical signalsfrom the cameras 5602, 5604 are absent for longer than a thresholdinterval.

It will be appreciated that the figures shown in FIG. 56 areillustrative. In some implementations, it may be desirable to house theenvironment 5600 in a differently shaped enclosure or integrated withina larger component or assembly. Furthermore, the number and type ofimage sensors, motion detectors, illumination sources, and so forth areshown schematically for clarity, but neither the size nor the number isthe same in all implementations.

Referring now to FIG. 57 , which shows a simplified block diagram of acomputer system 5700 for implementing gesture recognition system 5606.Computer system 5700 includes a processor 5702, a memory 5704, a motiondetector and camera interface 5706, a presentation interface 5620,speaker(s) 5709, a microphone(s) 5710, and a wireless interface 5711.Memory 5704 can be used to store instructions to be executed byprocessor 5702 as well as input and/or output data associated withexecution of the instructions. In particular, memory 5704 containsinstructions, conceptually illustrated as a group of modules describedin greater detail below, that control the operation of processor 5702and its interaction with the other hardware components. An operatingsystem directs the execution of low-level, basic system functions suchas memory allocation, file management and operation of mass storagedevices. The operating system may be or include a variety of operatingsystems such as Microsoft WINDOWS operating system, the Unix operatingsystem, the Linux operating system, the Xenix operating system, the IBMAIX operating system, the Hewlett Packard UX operating system, theNovell NETWARE operating system, the Sun Microsystems SOLARIS operatingsystem, the OS/2 operating system, the BeOS operating system, theMACINTOSH operating system, the APACHE operating system, an OPENACTIONoperating system, iOS, Android or other mobile operating systems, oranother operating system of platform.

The computing environment may also include otherremovable/non-removable, volatile/nonvolatile computer storage media.For example, a hard disk drive may read or write to non-removable,nonvolatile magnetic media. A magnetic disk drive may read from or writeto a removable, nonvolatile magnetic disk, and an optical disk drive mayread from or write to a removable, nonvolatile optical disk such as aCD-ROM or other optical media. Other removable/non-removable,volatile/nonvolatile computer storage media that can be used in theexemplary operating environment include, but are not limited to,magnetic tape cassettes, flash memory cards, digital versatile disks,digital video tape, solid state RAM, solid state ROM, and the like. Thestorage media are typically connected to the system bus through aremovable or non-removable memory interface.

Processor 5702 may be a general-purpose microprocessor, but depending onimplementation can alternatively be a microcontroller, peripheralintegrated circuit element, a CSIC (customer-specific integratedcircuit), an ASIC (application-specific integrated circuit), a logiccircuit, a digital signal processor, a programmable logic device such asan FPGA (field-programmable gate array), a PLD (programmable logicdevice), a PLA (programmable logic array), an RFID processor, smartchip, or any other device or arrangement of devices that are capable ofimplementing the actions of the processes of the technology disclosed.

Motion detector and camera interface 5706 can include hardware and/orsoftware that enables communication between computer system 5700 andcameras 5602, 5604, as well as sensors 5608, 5610 (see FIG. 56 ). Thus,for example, motion detector and camera interface 5706 can include oneor more camera data ports 5716, 5718 and motion detector ports 5717,5719 to which the cameras and motion detectors can be connected (viaconventional plugs and jacks), as well as hardware and/or softwaresignal processors to modify data signals received from the cameras andmotion detectors (e.g., to reduce noise or reformat data) prior toproviding the signals as inputs to a motion-capture (“mocap”) program5714 executing on processor 5702. In some implementations, motiondetector and camera interface 5706 can also transmit signals to thecameras and sensors, e.g., to activate or deactivate them, to controlcamera settings (frame rate, image quality, sensitivity, etc.), tocontrol sensor settings (calibration, sensitivity levels, etc.), or thelike. Such signals can be transmitted, e.g., in response to controlsignals from processor 5702, which may in turn be generated in responseto user input or other detected events.

Instructions defining mocap program 5714 are stored in memory 5704, andthese instructions, when executed, perform motion-capture analysis onimages supplied from cameras and audio signals from sensors connected tomotion detector and camera interface 5706. In one implementation, mocapprogram 5714 includes various modules, such as an object analysis module5722 and a path analysis module 5724. Object analysis module 5722 cananalyze images (e.g., images captured via interface 5706) to detectedges of an object therein and/or other information about the object'slocation. In some implementations, object detection module 5722 can alsoanalyze audio signals (e.g., audio signals captured via interface 5706)to localize the object by, for example, time distance of arrival,multilateration or the like. (“multilateration is a navigation techniquebased on the measurement of the difference in distance to two or morestations at known locations that broadcast signals at known times. SeeWikipedia, at<http://en.wikipedia.org/w/index.php?title=Multilateration&oldid=523281858>,on Nov. 16, 2012, 06:07 UTC). Path analysis module 5724 can track andpredict object movements in 3D based on information obtained via thecameras. Some implementations include an augmented reality (AR)/virtualreality (VR) environment 5600 provides integration of virtual objectsreflecting real objects (e.g., hand 5614) as well as synthesized objects5616 for presentation to user of device 5601 via presentation interface5620 to provide a personal virtual experience. One or more applications5730 can be loaded into memory 5704 (or otherwise made available toprocessor 5702) to augment or customize functioning of device 5601thereby enabling the system 5700 to function as a platform. Successivecamera images are analyzed at the pixel level to extract objectmovements and velocities. Audio signals place the object on a knownsurface, and the strength and variation of the signals can be used todetect object's presence. If both audio and image information issimultaneously available, both types of information can be analyzed andreconciled to produce a more detailed and/or accurate path analysis. Insome implementations, a video feed integrator provides integration oflive video feed from the cameras 5602, 5604 and one or more virtualobjects. Video feed integrator governs processing of video informationfrom disparate types of cameras 5602, 5604. For example, informationreceived from pixels sensitive to IR light and from pixels sensitive tovisible light (e.g., RGB) can be separated by integrator and processeddifferently. Image information from IR sensors can be used for gesturerecognition, while image information from RGB sensors can be provided asa live video feed via presentation interface 5620. Information from onetype of sensor can be used to enhance, correct, and/or corroborateinformation from another type of sensor. Information from one type ofsensor can be favored in some types of situational or environmentalconditions (e.g., low light, fog, bright light, and so forth). Thedevice can select between providing presentation output based upon oneor the other types of image information, either automatically or byreceiving a selection from the user. Integrator in conjunction withAR/VR environment 5600 control the creation of the environment presentedto the user via presentation interface 5620.

Presentation interface 5620, speakers 5709, microphones 5710, andwireless network interface 5711 can be used to facilitate userinteraction via device 5601 with computer system 5700. These componentscan be of generally conventional design or modified as desired toprovide any type of user interaction. In some implementations, resultsof motion capture using motion detector and camera interface 5706 andmocap program 5714 can be interpreted as user input. For example, a usercan perform hand gestures or motions across a surface that are analyzedusing mocap program 5714, and the results of this analysis can beinterpreted as an instruction to some other program executing onprocessor 5702 (e.g., a web browser, word processor, or otherapplication). Thus, by way of illustration, a user might use upward ordownward swiping gestures to “scroll” a webpage currently displayed tothe user of device 5601 via presentation interface 5620, to use rotatinggestures to increase or decrease the volume of audio output fromspeakers 5709, and so on. Path analysis module 5724 may represent thedetected path as a vector and extrapolate to predict the path, e.g., toimprove rendering of action on device 5601 by presentation interface5620 by anticipating movement.

It will be appreciated that computer system 5700 is illustrative andthat variations and modifications are possible. Computer systems can beimplemented in a variety of form factors, including server systems,desktop systems, laptop systems, tablets, smart phones or personaldigital assistants, and so on. A particular implementation may includeother functionality not described herein, e.g., wired and/or wirelessnetwork interfaces, media playing and/or recording capability, etc. Insome implementations, one or more cameras and two or more microphonesmay be built into the computer rather than being supplied as separatecomponents. Further, an image or audio analyzer can be implemented usingonly a subset of computer system components (e.g., as a processorexecuting program code, an ASIC, or a fixed-function digital signalprocessor, with suitable I/O interfaces to receive image data and outputanalysis results).

While computer system 5700 is described herein with reference toparticular blocks, it is to be understood that the blocks are definedfor convenience of description and are not intended to imply aparticular physical arrangement of component parts. Further, the blocksneed not correspond to physically distinct components. To the extentthat physically distinct components are used, connections betweencomponents (e.g., for data communication) can be wired and/or wirelessas desired. Thus, for example, execution of object detection module 5722by processor 5702 can cause processor 5702 to operate motion detectorand camera interface 5706 to capture images and/or audio signals of anobject traveling across and in contact with a surface to detect itsentrance by analyzing the image and/or audio data.

In one implementation, the neural network module 5726 stores theconvolutional neural network 101, which operates in conjunction with theAR/VR environment 5600 and applications 5730.

Conclusion and Additional Implementations

We describe a system and various implementations for detecting handposes and gestures using a convolutional neural network.

Some additional implementations and features include:

-   -   Because all the pose estimation networks use the same coordinate        system and feature extractor, the disclosed convolutional neural        network is highly flexible to computation requirements and        demands for a desired level of accuracy and robustness.    -   In some implementations, a model-parallel training is used,        which automatically performs hyper-parameter sweeps over the        learning rate and batch size to determine the optimal settings        for a particular dataset and network architecture.    -   In some implementations, an adaptive algorithm is used, which        reduces the learning rate for a particular training job over        time in order to precisely specify an optimal network instead of        overshooting.    -   In some implementations, the technology disclosed provides        greater robustness to cluttered backgrounds and ambient light        interference (e.g., bright background scenes).    -   In some implementations, the technology disclosed provides        enhanced tracking range that extends to the full length of the        arms.    -   In some implementations, the technology disclosed provides        faster initialization for splayed hands and pointing fingers.    -   In some implementations, the technology disclosed accurately and        precisely tracks free form gestures in real time with negligible        latency.    -   In some implementations, the technology disclosed accurately and        precisely tracks varied complex gestures like grab-and-drop        interactions.    -   In some implementations, the technology disclosed reduces the        overall CPU usage suitable for embedded systems.    -   In some implementations, the technology disclosed provides        enhanced finger flexibility for better tracking of hand poses.    -   In some implementations, the technology disclosed provides for        improved handling of occluded hand poses.    -   In some implementations, the technology disclosed provides        image-based tracking using minimally processed image features to        estimate hand motion.    -   In some implementations, the technology disclosed simultaneously        estimates both rigid and non-rigid states of a hand.    -   In some implementations, the technology disclosed provides        improved tracking on the edge of the field of view.

Some particular implementations and features are described in thefollowing discussion.

In one implementation, described is method of preparing a plurality ofneural network systems to recognize hand positions. The method includesgenerating from 100,000 to 1 billion simulated hand position images,each hand position image labeled with 15 to 45 hand position parameters,the simulated hand position images organized as gesture sequences,applying a multilayer convolution and pooling processor and producingreduced dimensionality images from the simulated hand position images,training a first set of atemporal generalist neural networks with thesimulated hand position images to produce estimated hand positionparameters, using the reduced dimensionality images and the labeled handposition parameters for the reduced dimensionality images, subdividingthe simulated hand position images into 5 to 250 overlapping specialistcategories and training 5 to 250 corresponding atemporal specialistneural networks to produce estimated hand position parameters, traininga first set of atemporal specialist neural networks using the reduceddimensionality images from the corresponding specialist categories usingthe reduced dimensionality images from the simulated hand positionimages and the labeled hand position parameters for the reduceddimensionality images and saving parameters from training the atemporalgeneralist neural networks and the atemporal specialist neural networksin tangible machine readable memory for use in image recognition.

The method described in this section and other sections of thetechnology disclosed can include one or more of the following featuresand/or features described in connection with additional methodsdisclosed. In the interest of conciseness, the combinations of featuresdisclosed in this application are not individually enumerated and arenot repeated with each base set of features. The reader will understandhow features identified in this method can readily be combined with setsof base features identified as implementations such as convolutionalneural network, master or generalists networks, expert or specialistsnetworks, hand pose estimation, outlier-robust covariance propagation,experimental results, augmented reality (AR)/virtual reality (VR)interactions, generating training data, computer graphics simulator,gesture recognition, etc.

In one implementation, the simulated hand position images arestereoscopic images with depth map information. In anotherimplementation, the hand position parameters are a plurality of jointlocations in three-dimensional (3D) space. In yet anotherimplementation, the hand position parameters are a plurality of jointangles in three-dimensional (3D) space. In yet another implementation,the hand position parameters are a plurality of hand skeleton segmentsin three-dimensional (3D) space.

In some implementations, the overlapping specialist categories aregenerated using unsupervised classification. In one implementation, thegeneralist neural networks are trained an entire dataset of simulatedhand position images and the specialist neural networks are trained onparts of the dataset corresponding to the specialist categories. Inother implementations, the method includes calculating at least onecharacterization for each of the specialist neural networks thatpositions a particular specialist neural networks in distinction fromother specialist neural networks.

In some implementations, the method includes receiving a first set ofhand position parameters from one or more trained generalist neuralnetworks and identifying specialist categories with centroids proximateto the received hand position parameter, receiving a second set of handposition parameters from a multitude of trained specialist neuralnetworks corresponding to the identified specialist categories andcombining the first and second set of hand position parameters togenerate a final hand pose estimate.

In some implementations, the method includes combining the first andsecond set of hand position parameters to generate a final hand poseestimate using an outlier-robust covariance propagation scheme. In oneimplementation, each of the generalist and specialist neural networksgenerate 84 outputs representing 28 hand joint locations inthree-dimensional (3D) space.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

In another implementation, described is a method of preparing aplurality of neural network systems to recognize hand positions. Themethod includes generating from 100,000 to 1 billion simulated handposition images, each hand position image labeled with 15 to 45 handposition parameters, the simulated hand position images organized asgesture sequences, applying a multilayer convolution and poolingprocessor and producing reduced dimensionality images from the simulatedhand position images, training a first set of temporal generalist neuralnetworks with the simulated hand position images to produce estimatedhand position parameters, using pairs of first and second reduceddimensionality images, estimated or actual hand position parameters forthe first reduced dimensionality image, image data for the secondreduced dimensionality image, and the labeled hand position parametersfor the second reduced dimensionality image, subdividing the simulatedhand position images into 5 to 250 overlapping specialist categories andtraining 5 to 250 corresponding temporal specialist neural networks toproduce estimated hand position parameters and training a first set oftemporal specialist neural networks using pairs of first and secondreduced dimensionality images from the corresponding specialistcategories. In one implementation, training the first set of temporalspecialist neural networks includes estimated or actual hand positionparameters for the first reduced dimensionality image, image data forthe second reduced dimensionality data and the labeled hand positionparameters for the second reduced dimensionality image. The methodfurther includes saving parameters from training the temporal generalistneural networks and the temporal specialist neural networks in tangiblemachine readable memory for use in image recognition.

The method described in this section and other sections of thetechnology disclosed can include one or more of the following featuresand/or features described in connection with additional methodsdisclosed. In the interest of conciseness, the combinations of featuresdisclosed in this application are not individually enumerated and arenot repeated with each base set of features. The reader will understandhow features identified in this method can readily be combined with setsof base features identified as implementations such as convolutionalneural network, master or generalists networks, expert or specialistsnetworks, hand pose estimation, outlier-robust covariance propagation,experimental results, augmented reality (AR)/virtual reality (VR)interactions, generating training data, computer graphics simulator,gesture recognition, etc.

In one implementation, the temporal generalist neural networks and thetemporal specialist neural networks are recursive neural networks (RNN)based on long short term memory (LSTM). In another implementation, thetemporal generalist neural networks and the temporal specialist neuralnetworks are trained using a combination of current simulated handposition images and additional noise hand position data. In yet anotherimplementation, the temporal generalist neural networks and the temporalspecialist neural networks are trained using a series of simulated handposition images that are temporally linked as gesture sequencesrepresenting real world hand gestures. In a further implementation, thetemporal generalist neural networks and the temporal specialist neuralnetworks, during testing, utilize a combination of a current simulatedhand position image and a series of prior estimated hand positionparameters temporally linked in previous frames to generate a currentset of hand position parameters.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

In yet another implementation, described is a method of recognizing handpositions in image sequences, including occluded portions of the handpositions. The method includes receiving a temporal sequence of imagesfrom a field of view, applying a multilayer convolution and poolingprocessor and producing reduced dimensionality images, includingsuccessive first and second reduced dimensionality images, from thetemporal sequence of images, processing a pair of first and secondreduced dimensionality images using a second temporal generalist neuralnetwork to produce estimated hand position parameters, using pairs offirst and second reduced dimensionality images, estimated hand positionparameters for the first reduced dimensionality image and image data forthe second reduced dimensionality data, and the labeled hand positionparameters for the second reduced dimensionality image, processing asecond image a first atemporal generalist neural network with thesimulated hand position images to produce estimated hand positionparameters, using the reduced dimensionality images and the labeled handposition parameters for the reduced dimensionality image, using theestimated hand position parameters from the first atemporal generalistneural network and the second temporal generalist neural network toselect among 5 to 250 overlapping specialist neural networks,reprocessing at least a second reduced dimensionality image using theselected specialist neural networks to estimate positions of between 15and 45 hand position parameter, including hand portions that areoccluded by other hand portions in the second reduced dimensionalityimage and saving parameters from training the atemporal generalistneural network, the temporal generalist neural network, the atemporalspecialist neural networks, and the atemporal specialist neural networksin tangible machine readable memory for use in image recognition.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

In one implementation, described is a method of preparing sample handpositions for training of neural network systems. The method includesaccessing simulation parameters that specify a range of hand positionsand position sequences, a range of hand anatomies, including palm size,fattiness, stubbiness, and skin tone and a range of backgrounds. Themethod also includes accessing a camera perspective specification thatspecifies a focal length, a field of view of the camera, a wavelengthsensitivity, field distortions and artificial lighting conditions. Themethod further includes generating between 100,000 and 1 billion handposition-hand anatomy-background simulations, each simulation labeledwith 15 to 45 hand position parameters, the simulations organized insequences, applying the camera perspective specification to render fromthe simulations at least a corresponding 100,000 to 1 billion simulatedhand position images and saving the simulated hand position images withthe labelled hand position parameters from the corresponding simulationsfor use in training a hand position recognition system.

The method described in this section and other sections of thetechnology disclosed can include one or more of the following featuresand/or features described in connection with additional methodsdisclosed. In the interest of conciseness, the combinations of featuresdisclosed in this application are not individually enumerated and arenot repeated with each base set of features. The reader will understandhow features identified in this method can readily be combined with setsof base features identified as implementations such as convolutionalneural network, master or generalists networks, expert or specialistsnetworks, hand pose estimation, outlier-robust covariance propagation,experimental results, augmented reality (AR)/virtual reality (VR)interactions, generating training data, computer graphics simulator,gesture recognition, etc.

In one implementation, the simulated hand position images arestereoscopic images with depth map information. In anotherimplementation, the simulated hand position images are binocular pairsof images. In another implementation, the hand position parameters are aplurality of joint locations in three-dimensional (3D) space. In yetanother implementation, the hand position parameters are a plurality ofjoint angles in three-dimensional (3D) space. In yet anotherimplementation, the hand position parameters are a plurality of handskeleton segments in three-dimensional (3D) space.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

In another implementation, described is a method of preparing samplehand positions for training of neural network systems. The methodincludes generating ground truth simulated stereoscopic hand imagesusing a computer graphic simulator, extracting stereoscopic handboundaries for the hand images and aligning the hand boundaries withhand centers included in the hand images, generating translated, rotatedand scaled variants of the hand boundaries and applying Gaussianjittering to the variants, extracting hand regions from the jitteredvariants of the hand boundaries, computing ground truth pose vectors forthe hand regions using the computer graphic simulator and storing thepose vectors in tangible machine readable memory as output labels forthe stereoscopic hand images for use in image recognition.

The method described in this section and other sections of thetechnology disclosed can include one or more of the following featuresand/or features described in connection with additional methodsdisclosed. In the interest of conciseness, the combinations of featuresdisclosed in this application are not individually enumerated and arenot repeated with each base set of features. The reader will understandhow features identified in this method can readily be combined with setsof base features identified as implementations such as convolutionalneural network, master or generalists networks, expert or specialistsnetworks, hand pose estimation, outlier-robust covariance propagation,experimental results, augmented reality (AR)/virtual reality (VR)interactions, generating training data, computer graphics simulator,gesture recognition, etc.

In one implementation, the computer graphic simulator generatesthree-dimensional (3D) simulated hands in mesh models and/or capsulehand skeleton models. In another implementation, the computer graphicsimulator generates a simulated coordinate system to determine handposition parameters of a simulated hand in three-dimensional (3D). Inyet another implementation, the computer graphic simulator generates asimulated perspective of a simulated gesture recognition system todetermine hand position parameters of a simulated hand inthree-dimensional (3D). In some implementations, the ground truth posevectors are 84 dimensional representing 28 hand joints inthree-dimensional (3D) space.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

In one implementation, described is a method of determining a hand poseusing neural network systems. The method includes receiving a first setof estimates of hand position parameters from multiple generalist neuralnetworks and/or specialist neural networks for each of a plurality ofhand joints, for each individual hand joint, simultaneously determininga principal distribution of the first set of estimates and receiving asecond set of estimates of hand position parameters from the generalistneural networks and/or specialist neural networks for each of theplurality of hand joints. The method also includes, for each individualhand joint, simultaneously, calculating a similarity measure between thesecond set of estimates and the principal distribution of the first setof estimates, identifying outliers and inliers in the second set ofestimates based on the similarity measure, calculating contributionweights of the outliers and the inliers based on the similarity measureand determining a principal distribution of the second set of estimatesbased on the contribution weights of the outliers and inliers.

The method described in this section and other sections of thetechnology disclosed can include one or more of the following featuresand/or features described in connection with additional methodsdisclosed. In the interest of conciseness, the combinations of featuresdisclosed in this application are not individually enumerated and arenot repeated with each base set of features. The reader will understandhow features identified in this method can readily be combined with setsof base features identified as implementations such as convolutionalneural network, master or generalists networks, expert or specialistsnetworks, hand pose estimation, outlier-robust covariance propagation,experimental results, augmented reality (AR)/virtual reality (VR)interactions, generating training data, computer graphics simulator,gesture recognition, etc.

In some implementations, the method includes determining a hand pose byminimizing an approximation error between principal distributions ofeach of the hand joints. In another implementation, the hand positionparameters are a plurality of joint locations in three-dimensional (3D)space. In yet another implementation, the hand position parameters are aplurality of joint angles in three-dimensional (3D) space. In yetanother implementation, the hand position parameters are a plurality ofhand skeleton segments in three-dimensional (3D) space.

In some implementations, the principal distribution is a covariancematrix of the hand position parameter estimates. In otherimplementations, the similarity measure is a Mahalanobis distance fromthe principal distribution. In yet other implementations, the similaritymeasure is a projection statistic from the principal distribution.

In some implementations, the covariance matrix is determined using aKalman filter operation. In other implementations, the covariance matrixis updated between frames based on contribution weights of outliers andinliers of a current set of estimates of hand position parameters. Inyet other implementations the contribution weights are determined byconverting the similarity measure into probability distributions.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

In yet another implementation, described is a method of initializing ahand for neural network systems to recognize hand positions. The methodincludes detecting a hand in a field of view of at least one camera andcapturing stereoscopic images of the hand, generating feature maps fromthe stereoscopic images based on parallax and identifying one or moretwo-dimensional (2D) candidate regions of interest (ROI) in the featuremaps, determining a depth parameter for each of the candidate ROI byconverting the 2D candidate ROI into one-dimensional (1D) waveformsignals and convolving the 1D waveform signals across one of thestereoscopic images, extracting hand regions from the candidate ROIbased on a rotated principal orientation of pixel data in each of thecandidate ROI, subjecting the extracted hand regions to a plurality ofhand-heuristic analysis and feeding the hand regions and results of theanalysis to a hand classifier neural network and for a particular handregion qualified by the hand classifier neural network, rendering athree-dimensional (3D) virtual hand based on a 2D position and depthparameter of a corresponding candidate region of interest.

In one implementation, the hand-heuristic analysis determinesconsistency of the extracted hand regions with hand anatomies. Inanother implementation, the hand-heuristic analysis determines whetherthe detected hand is positioned above another previously detected handbased on a 2D position and depth parameter of the particular handregion. In yet another implementation, the hand-heuristic analysisdetermines whether the detected hand is a right hand or a left handbased on an estimated trajectory of the particular hand region.

In some implementations, the feature maps are at least one of parallaxmaps, low resolution saliency maps and disparity maps. In otherimplementations, the 1D waveform signals are generated using at leastone of normalized cross-correlation (NCC) and weighted NCC. In yet otherimplementations, the method includes performing an in-plane rotation togenerate upright hand regions using a combination of a principalorientation vector determined from a gradient direction of the pixeldata and at least one outward normal vector projecting from the handregions onto a camera plane.

Other implementations may include a computer implemented system toperform any of the methods described above, the system including aprocessor, memory coupled to the processor, and computer instructionsloaded into the memory. Yet another implementation may include atangible computer readable storage medium impressed with computerprogram instructions; the instructions, when executed on a processorcause a computer to implement any of the methods described above.

The terms and expressions employed herein are used as terms andexpressions of description and not of limitation, and there is nointention, in the use of such terms and expressions, of excluding anyequivalents of the features shown and described or portions thereof. Inaddition, having described certain implementations of the technologydisclosed, it will be apparent to those of ordinary skill in the artthat other implementations incorporating the concepts disclosed hereincan be used without departing from the spirit and scope of thetechnology disclosed. Accordingly, the described implementations are tobe considered in all respects as only illustrative and not restrictive.

What is claimed is:
 1. A method of determining a hand pose using neuralnetwork systems, the method including: receiving a first set ofestimates of hand position parameters from multiple generalist neuralnetworks and/or specialist neural networks for each of a plurality ofhand joints; for each individual hand joint, simultaneously determininga principal distribution of the first set of estimates; receiving asecond set of estimates of hand position parameters from the generalistneural networks and/or specialist neural networks for each of theplurality of hand joints; and for each individual hand joint,simultaneously: calculating a similarity measure between the second setof estimates and the principal distribution of the first set ofestimates; identifying select estimates in the second set of estimatesbased on the similarity measure; calculating contribution weights of theselect estimates based on the similarity measure; and determining aprincipal distribution of the second set of estimates based on thecontribution weights of the select estimates.
 2. The method of claim 1,further including identifying outliers and inliers as select estimates.3. The method of claim 1, further including determining a hand pose byminimizing an approximation error between principal distributions ofeach of the hand joints.
 4. The method of claim 1, wherein the handposition parameters of at least one of the first set of estimates andthe second set of estimates are a plurality of joint locations inthree-dimensional (3D) space.
 5. The method of claim 1, wherein the handposition parameters of at least one of the first set of estimates andthe second set of estimates are a plurality of joint angles inthree-dimensional (3D) space.
 6. The method of claim 1, wherein the handposition parameters of at least one of the first set of estimates andthe second set of estimates are a plurality of hand skeleton segments inthree-dimensional (3D) space.
 7. The method of claim 1, wherein theprincipal distribution is a covariance matrix of the hand positionparameter estimates.
 8. The method of claim 1, wherein the similaritymeasure is a Mahalanobis distance from the principal distribution. 9.The method of claim 1, wherein the similarity measure is a projectionstatistic from the principal distribution.
 10. The method of claim 7,wherein the covariance matrix is determined using a Kalman filteroperation.
 11. The method of claim 7, wherein the covariance matrix isupdated between frames based on contribution weights of outliers andinliers of a current set of estimates of hand position parameters. 12.The method of claim 1, wherein the contribution weights are determinedby converting the similarity measure into probability distributions. 13.A non-transitory computer readable storage medium impressed withcomputer program instructions to determine a hand pose using neuralnetwork systems, the instructions, when executed on a processor,implement a method comprising: receiving a first set of estimates ofhand position parameters from multiple generalist neural networks and/orspecialist neural networks for each of a plurality of hand joints; foreach individual hand joint, simultaneously determining a principaldistribution of the first set of estimates; receiving a second set ofestimates of hand position parameters from the generalist neuralnetworks and/or specialist neural networks for each of the plurality ofhand j oints; and for each individual hand joint, simultaneously:calculating a similarity measure between the second set of estimates andthe principal distribution of the first set of estimates; identifyingoutliers and inliers in the second set of estimates based on thesimilarity measure; calculating contribution weights of the outliers andthe inliers based on the similarity measure; and determining a principaldistribution of the second set of estimates based on the contributionweights of the outliers and inliers.
 14. The non-transitory computerreadable storage medium of claim 13, implementing the method furthercomprising determining a hand pose by minimizing an approximation errorbetween principal distributions of each of the hand joints.
 15. Thenon-transitory computer readable storage medium of claim 13, wherein thehand position parameters of at least one of the first set of estimatesand the second set of estimates are a plurality ofjoint locations inthree-dimensional (3D) space.
 16. The non-transitory computer readablestorage medium of claim 13, wherein the hand position parameters of atleast one of the first set of estimates and the second set of estimatesare a plurality ofjoint angles in three-dimensional (3D) space.
 17. Thenon-transitory computer readable storage medium of claim 13, wherein thehand position parameters of at least one of the first set of estimatesand the second set of estimates are a plurality of hand skeletonsegments in three-dimensional (3D) space.
 18. The non-transitorycomputer readable storage medium of claim 13, wherein the principaldistribution is a covariance matrix of the hand position parameterestimates.
 19. The non-transitory computer readable storage medium ofclaim 13, wherein the similarity measure is a Mahalanobis distance fromthe principal distribution.
 20. The non-transitory computer readablestorage medium of claim 13, wherein the contribution weights aredetermined by converting the similarity measure into probabilitydistributions.
 21. A system including one or more processors coupled tomemory, the memory loaded with computer instructions to determine a handpose using neural network systems, the instructions, when executed onthe processors, implement actions comprising: receiving a first set ofestimates of hand position parameters from multiple generalist neuralnetworks and/or specialist neural networks for each of a plurality ofhand joints; for each individual hand joint, simultaneously determininga principal distribution of the first set of estimates; receiving asecond set of estimates of hand position parameters from the generalistneural networks and/or specialist neural networks for each of theplurality of hand joints; and for each individual hand joint,simultaneously: calculating a similarity measure between the second setof estimates and the principal distribution of the first set ofestimates; identifying outliers and inliers in the second set ofestimates based on the similarity measure; calculating contributionweights of the outliers and the inliers based on the similarity measure;and determining a principal distribution of the second set of estimatesbased on the contribution weights of the outliers and inliers.
 22. Amethod of determining a hand pose using neural network systems, themethod including: receiving (i) a first set of estimates of handposition parameters from multiple generalist neural networks and/orspecialist neural networks for each of a plurality of hand joints; (ii)a principal distribution of the first set of estimates determined foreach individual hand joint; and (iii) a second set of estimates of handposition parameters from the generalist neural networks and/orspecialist neural networks for each of the plurality of hand joints; andfor each individual hand joint: calculating a similarity measure betweenthe second set of estimates and the principal distribution of the firstset of estimates; identifying select estimates in the second set ofestimates based on the similarity measure; calculating contributionweights of the select estimates based on the similarity measure; anddetermining a principal distribution of the second set of estimatesbased on the contribution weights of the select estimates.
 23. A methodof determining a hand pose using neural network systems, the methodincluding: receiving a principal distribution of a second set ofestimates of hand position parameters having been determined based oncontribution weights calculated of select estimates identified in thesecond set of estimates based on a calculated similarity measurecalculated for individual ones of a plurality of hand joints between thesecond set of estimates and a principal distribution of a first set ofestimates; wherein the (i) a first set of estimates of hand positionparameters for individual ones of a plurality of hand joints and the(ii) the second set of estimates of hand position parameters forindividual ones of a plurality of hand joints are obtained from multiplegeneralist neural networks and/or specialist neural networks, and usingthe received principle distribution to inform a hand pose based upon thefirst set of estimates of hand position parameters and the second set ofhand position parameters.
 24. A system including one or more processorscoupled to memory, the memory loaded with computer instructions todetermine a hand pose using neural network systems, the instructions,when executed on the processors, implement actions comprising: obtaininga principal distribution of a second set of estimates of hand positionparameters having been determined based on contribution weightscalculated of select estimates identified in the second set of estimatesbased on a calculated similarity measure calculated for individual onesof a plurality of hand joints between the second set of estimates and aprincipal distribution of a first set of estimates; wherein the (i) afirst set of estimates of hand position parameters for individual onesof a plurality of hand joints and the (ii) the second set of estimatesof hand position parameters for individual ones of a plurality of handjoints are obtained from multiple generalist neural networks and/orspecialist neural networks, and using the received principledistribution to inform a hand pose based upon the first set of estimatesof hand position parameters and the second set of hand positionparameters.